Aarushhh/wikipedia-simple-splitted huggingface dataset:
Francisco Brennand, or Francisco de Paula de Almeida Brennand, (June 11, 1927 – December 19, 2019) was a Brazilian sculptor. He worked in several different media. He was best known for his work in ceramic sculpture. Brennand was born in Recife, Pernambuco. He also used ceramics to create floor and wall tiles for construction.

Brennand died on December 19, 2019, in Recife of respiratory tract infection-related problems at the age of 92.

Exhibits
Propriedade Santos Cosme e Damião, Várzea (the artist's studio)
Marco Zero square in Recife Antigo, Recife (the Sculpture Park)
18th São Paulo Art Biennial – 1985
20th São Paulo Art Biennial – 1989
 Esculturas 1974–1998 at the Pinacoteca do Estado de São Paulo – 1998
Casa França-Brasil, Rio de Janeiro – 2000
Esculturas at the Oscar Niemeyer Museum, Curitiba – 2004

References

Other websites
  Brennand's official homepage 
  Brennand's diary extracts
 Photographs of Oficina Brennand by Jonathan Flaum
1927 births
2019 deaths
Infectious disease deaths in Brazil
Deaths from respiratory tract infection
Brazilian artists
Sculptors
Protopresbyter (Archpriest) Fr. George Metallinos (in Greek π. Γεώργιος Μεταλληνός; 11 March 1940 – 19 December 2019) was a Greek theologian, priest, historian, author and professor. Metallinos was born in Corfu, Greece.

In 1971, he was ordained a member of the clergy and became Doctor of Theology (University of Athens) and Doctor of Philosophy - History (University of Cologne). In 1984 he became Professor at the School of Theology of the University of Athens, teaching History of Spirituality during the Post-Byzantine Period, History and Theology of Worship, and Byzantine History.

Metallinos died in Athens on 19 December 2019 at the age of 79.

References
References

Other websites
 The Resurrection of Christ is the Annihilation of Death by Protopresbyter Fr. George Metallinos.
 ''Orthodox Spirituality - Mutual Concession of Present and Future Life by Protopresbyter Fr. George Metallinos.
 Orthodoxy as Therapy by Protopresbyter George Metallinos.
 Orthodoxy's Worship  by Protopresbyter George Metallinos.
 ''Philokalian Distinction between Orthodoxy and Heresy  by Protopresbyter George Metallinos.
 ''The Importance of Hesychasm in the History of the Roman Nation by Protopresbyter George Metallinos.

1940 births
2019 deaths
Eastern Orthodox priests
Greek academics
Greek historians
Christian theologians
Greek writers
Corfu
Shahdon Shane Andre Winchester (8 January 1992 – 19 December 2019) was a Trinidadian professional footballer. He played as a winger for the Trinidad and Tobago national team from 2010 through 2017.

Winchester was one of four people killed in a car crash on 19 December 2019 in Gasparillo, catching on fire, aged 27.

References

1992 births
2019 deaths
Road accident deaths
Trinidad and Tobago footballers
Alba Maria Zaluar (2 June 1942 – 19 December 2019) was a Brazilian anthropologist. Her works focused in anthropology of violence. In 1984, she got her PhD in social Anthropology at the Federal University of Rio de Janeiro. Zaluar was born in Rio de Janeiro. 

Zaluar worked as invited professor in the State University of Campinas, and as professor in the Federal University of Rio de Janeiro, where she coordinated the "Núcleo de Pesquisas da Violência" (NUPEVI), located in the Institute of Social Medicine.

Zaluar died on 19 December 2019 in Rio de Janeiro of pancreatic cancer, aged 77.

References

1942 births
2019 deaths
Deaths from pancreatic cancer
Anthropologists
Brazilian educators
Writers from Rio de Janeiro
William Shield McFeely (September 25, 1930 – December 11, 2019) was an American historian and educator. In 1982, he won the Pulitzer Prize. He worked at Yale University, the University of Georgia and at Harvard University. McFeely was known for his biographies about Ulysses S. Grant and the Reconstruction era.

Life
He was born in New York City. McFeely studied at Amherst College and at Yale University.

McFeely taught at Yale until 1970, during the Civil Rights Movement and Black Power movements. One of his black students in his class was Henry Louis Gates Jr..

McFeely was known for his Pulitzer Prize-winning 1981 biography of Ulysses S. Grant. His works also focused on the Reconstruction era, and for the field of African-American history.  He retired as the Abraham Baldwin Professor of the Humanities emeritus at the University of Georgia in 1997. He began working for Harvard University in 2006.
McFeely died of idiopathic pulmonary fibrosis on December 11, 2019 at his home in Sleepy Hollow, New York at the age of 89.

Awards and honors
1982 Pulitzer Prize for Biography or Autobiography for  Grant: A Biography
1982  Francis Parkman Prize for Grant: A Biography
Member, American Academy of Arts and Sciences (since 1987)
The Lincoln Prize 1991 for Frederick Douglass (based upon the life of Frederick Douglass).
1992 Avery O. Craven Award from the Organization of American Historians.

Some works
 Yankee Stepfather: General O.O. Howard and the Freedmen (W. W. Norton, 1968)
 Grant: A Biography (W. W. Norton, 1981)
 Frederick Douglass (W. W. Norton, 1990)
 Sapelo's People: A Long Walk into Freedom (W. W. Norton, 1994)
 Proximity to Death (W. W. Norton, 2000)
 Portrait: The Life of Thomas Eakins (W. W. Norton, 2007)

References

Other websites
 

Pulitzer Prize winners
1930 births
2019 deaths
Deaths from idiopathic pulmonary fibrosis
American historians
Educators from New York City
Writers from New York City
Black Power is a political slogan and a name for many ideologies that are pro-African-American identity. It is used mainly in the United States. The Black Power movement was created in the late 1960s and early 1970s.

References

American civil rights
Clive Anthony Lewis (born 11 September 1971) is a British Labour politician and journalist. He has been the Member of Parliament (MP) for Norwich South since winning the seat at the 2015 general election.

Lewis was appointed by Jeremy Corbyn's Shadow Cabinet as Shadow Secretary of State for Defence in June 2016, and later appointed Shadow Secretary of State for Business, Energy and Industrial Strategy in the October 2016 reshuffle.

In December 2019, Lewis announced his candidacy for Leader of the Labour Party in the 2020 leadership election. He dropped out from the race on 13 January 2020.

References

1971 births
Living people
Journalists from London
UK MPs 2015–2017
UK MPs 2017–2019
UK MPs 2019–present
Labour Party (UK) MPs
Politicians from London
Lisa Eva Nandy (born 9 August 1979) is a British Labour Party politician. She has been Member of Parliament (MP) for Wigan since 2010. She was Shadow Secretary of State for Energy and Climate Change from September 2015 until June 2016. She became the Shadow Secretary of State for Foreign and Commonwealth Affairs on 5 April 2020.

Nandy ran in the 2020 Labour Party leadership election. Out of three candidates she came in third place and received 79,597 votes, representing 16.2% of the total vote.

A day after the 2020 Labour Party leadership election on 5 April 2020, the winning candidate, Keir Starmer, appointed Nandy in the shadow cabinet in the role of Shadow Secretary of State for Foreign and Commonwealth Affairs.

References

1979 births
Living people
UK MPs 2010–2015
UK MPs 2015–2017
UK MPs 2017–2019
UK MPs 2019–present
Labour Party (UK) MPs

Politicians from Manchester
Sir Keir Rodney Starmer  (born 2 September 1962) is a British politician who has served as leader of the Labour Party and Leader of the Opposition since 2020. Since 2015 he has been the Member of Parliament (MP) for Holborn and St Pancras, a constituency of the UK Parliament in Inner London. He has been re-elected as the constituency's MP in the 2017 general election, and 2019 general election.

Starmer was the Shadow Secretary of State for Exiting the European Union in Jeremy Corbyn's Shadow Cabinet. He was Director of Public Prosecutions and Head of the Crown Prosecution Service from 2008 to 2013.
In January 2020, Starmer announced his candidacy for Labour Leader in the 2020 election. On 4 April 2020, Starmer was elected as leader of the Labour Party, and as the Labour had the second most number of seats in the House of Commons, this made him the Leader of the Opposition. He was elected as leader of the Labour Party in the first round of voting using the single transferable vote (stv) method of voting. Starmer won with 275,780 votes (56.2%). He got 40,417 (53.13%) of the  affiliates vote, 225,135 (56.07%) of the Labour Party members vote, and 10,228 (78.64%) of the registered supporters vote.

Personal Life 
Starmer is an atheist, but has said that he "does believe in faith", and its power to bring people together. His wife, Victoria Alexander, is Jewish, and thier two children are brought up in Jewish faith.

References
References

1962 births
Living people
Labour Party (UK) MPs
Leaders of the Labour Party (UK)
Leaders of the Opposition (United Kingdom)
Members of the British House of Commons for English constituencies
Politicians from London
Members of the Privy Council of the United Kingdom
UK MPs 2015–2017
UK MPs 2017–2019
UK MPs 2019–present

European Jews
Socialists
Atheists
Jonathan Michael Graham Ashworth (born 14 October 1978) is a British Labour and Co-operative Party politician. He has been a Member of Parliament for Leicester South since 2011, and is the current Shadow Secretary of State for Health and Social Care.

He worked as an adviser to Gordon Brown and head of party relations for Ed Miliband.

References

1978 births
Living people
Labour Party (UK) MPs
UK MPs 2010–2015
UK MPs 2015–2017
UK MPs 2017–2019
UK MPs 2019–present
Politicians from Greater Manchester
Daniel Owen Woolgar Jarvis,  (born 30 November 1972) is a British Labour Party politician.

From 1997 to 2011, he was in the Parachute Regiment, before being elected as the Member of Parliament (MP) for Barnsley Central in a by-election in 2011.

He was elected as Mayor of the Sheffield City Region in 2018.

References

1972 births
Living people
UK MPs 2010–2015
UK MPs 2015–2017
UK MPs 2017–2019
UK MPs 2019–present
Labour Party (UK) MPs
People from Nottingham

Directly elected British mayors
People from South Yorkshire
David Lindon Lammy  (born 19 July 1972) is a British Labour Party politician. He has been the Member of Parliament (MP) for Tottenham since 2000. He has been serving as Shadow Secretary of State for Foreign, Commonwealth and Development Affairs since 2021.

References

1972 births
Living people
Politicians from London
Labour Party (UK) MPs
UK MPs 1997–2001
UK MPs 2001–2005
UK MPs 2005–2010
UK MPs 2010–2015
UK MPs 2015–2017
UK MPs 2017–2019
UK MPs 2019–present
Black British people
Jessica Rose Phillips (; born 9 October 1981) is a British Labour Party politician. She has been the Member of Parliament (MP) for Birmingham Yardley since the 2015 general election.

In January 2020, Phillips briefly ran for Leader of the Labour Party in the 2020 leadership election.

References

1981 births
Living people
UK MPs 2015–2017
UK MPs 2017–2019
UK MPs 2019–present
Labour Party (UK) MPs
Politicians from Birmingham
Alumni of the University of Birmingham
Robert Geoffrey Burrow (born 26 September 1982) is an English former professional rugby league footballer. He spent 16 years playing for the Leeds Rhinos in the Super League, before retiring in 2017. 

He also played for England and Great Britain. Burrow was known for many years as "the smallest player in Super League". He won a total of 8 Super League championships, two Challenge Cups, been named to the Super League Dream Team on three occasions and won the Harry Sunderland Trophy twice.

In December 2019, Burrow announced that he was diagnosed with motor neurone disease.

References

Other websites
(archived by web.archive.org) Leeds Rhinos profile

1982 births
Living people
English rugby union players
Sportspeople from Yorkshire
Jason Eli Becker (born July 22, 1969) is an American musician, songwriter and composer. He is known for his albums Speed Metal Symphony in 1987, Go Off! in 1988, Perpetual Burn in 1988 and A Little Ain't Enough.

In the 1990s, Becker was diagnosed with amyotrophic lateral sclerosis.

References

Other websites
 Jason Becker's official website
 Becker's MySpace page
 Shrapnel Records official website
 Documentary film website 

1969 births
Living people
American rock guitarists
American composers
American songwriters
Musicians from California
Writers from California
People from Richmond, California
Ezio Bosso (; 13 September 1971 – 15 May 2020) was an Italian composer, classical musician and conductor. He was born in Turin.

On October 30, 2015 his first major studio album, The 12th Room, was released and peaked at number three on the Italian FIMI albums chart. Bosso has won several awards for his compositions, including the Australian Green Room Award, the Syracuse NY Award and two David di Donatello Awards.

In September 2019 Bosso announced that he was diagnosed with motor neurone disease. He died from the disease on 15 May 2020, aged 48.

References

1971 births
2020 deaths
Deaths from motor neurone disease
21st-century Italian composers
Italian conductors
Italian musicians
People from Turin
Orenthial James Brigance (born September 29, 1969) is a former football linebacker. He played in the Canadian Football League (CFL) and the National Football League (NFL). He is the senior advisor to player development for the Baltimore Ravens.

In May 2007, Brigance was diagnosed with amyotrophic lateral sclerosis.

References

Other websites
 Brigance Brigade official website

1969 births
Living people
American football linebackers
Baltimore Ravens players
BC Lions players
Miami Dolphins players
New England Patriots players
Sportspeople from Houston
St. Louis Rams players
Marián Čišovský (2 November 1979 – 28 June 2020) was a Slovak football defender. He played for Viktoria Plzeň.

On 5 August 2010 he scored the qualification goal in 93rd minute against MyPa in Europa League making it 3–3. Čišovský scored one goal in 2–0 won against Oţelul Galaţi.

In 2011, he was diagnosed with amyotrophic lateral sclerosis. He died from the disease on 28 June 2020, aged 40.

References

Other websites
  

1987 births
2020 deaths
Slovak footballers
Deaths from motor neurone disease
Rickey Dixon (December 26, 1966 – August 1, 2020) was an American cornerback  and special teams player. He played for the Oklahoma Sooners and later the National Football League’s Cincinnati Bengals and Los Angeles Raiders.

Dixon was elected to the College Football Hall of Fame in 2019.

Dixon was diagnosed with amyotrophic lateral sclerosis in 2014.  He died from the disease on August 1, 2020 in DeSoto, Texas at the age of 53.

References

Other websites
Rickey Dixon comes to terms with Cincinnati Bengals
Rickey Dixon: All-American at SoonerSports.com
Rickey Dixon – Jim Thorpe Award Winners at SoonerSports.com
Rickey Dixon Database Football

1966 births
2020 deaths
Deaths from motor neurone disease
American football cornerbacks
American football safeties
Cincinnati Bengals players
Oakland Raiders players
Sportspeople from Dallas
Victor S. Gilliam (July 21, 1953 – June 18, 2020) was an American politician and actor. He is a member of the Republican Party. He was in the Oregon House of Representatives from the 18th District from his appointment in January 2007 until his resignation in January 2017.

In November 2015, Gilliam was diagnosed with ALS. He died from the disease in Silverton, Oregon on June 18, 2020 at the age of 66.

References

Other websites
 Vic Gilliam's office website 
 Vic Gilliam's campaign website 
 The Oregonian Your Government: Vic Gilliam, R-Silverton Oregon House District 18

1953 births
2020 deaths
Deaths from motor neurone disease
State legislators of the United States
Actors from Ohio
Actors from Oregon
Politicians from Ohio
Politicians from Oregon
Republican Party (United States) politicians
Silverton is a city in Marion County, Oregon, United States.

References

Cities in Oregon
Euan MacDonald MBE is a Scottish businessman. He studied at the University of St Andrews and the University of Edinburgh. MacDonald created The Euan MacDonald Centre for Motor Neurone Disease Research in 2007 in partnership with the University of Edinburgh.

MacDonald was diagnosed with Motor Neurone Disease (MND) in October 2003.

In 2013, MacDonald co-founded the disabled access review website, Euan's Guide. In November 2014, MacDonald was named as one of the most influential disabled people in the UK.

References

Living people
Disability activists
Scottish businesspeople
British activists‎
1974 births
Club career
Born in Amsterdam, Rensenbrink started his career at DWS, an Amsterdam amateur club, before moving to Belgian side Club Brugge in 1969. Between 1971 and 1980 he played for Anderlecht where he enjoyed his greatest club successes. In total when in Belgium he twice won the Belgian Championships, the Belgian Cup five times and at European club level the European Cup Winners' Cup twice (in 1976 and 1978 as well as being runner-up in 1977). Rensenbrink delivered a notable performance in the 1976 final as Anderlecht ran out 4–2 winners against West Ham United. He scored two goals, one from the penalty spot and set up Francois Van der Elst for the fourth goal. Among his team mates was Dutch internationalist compatriot, Arie Haan. In 1980, he left Anderlecht and wound down his career with a spell at Portland Timbers in the NASL, followed by a brief stay with Toulouse in France in 1981.
International career
Rensenbrink made his international debut for the Netherlands national football team against Scotland in 1968, but picked up relatively few caps due to competition for the forward positions with Johan Cruijff and Piet Keizer. However, Rinus Michels included him for the 1974 FIFA World Cup squad that made the short trip to West Germany.
The Dutch side that took part in the 1974 FIFA World Cup were the pinnacle of Total Football. Most of the 1974 team were made up of players from Ajax and Feyenoord, so Rensenbrink was an outsider and was unfamiliar with playing the system. His preferred position was up front on the left, but that position was already Johan Cruijff's domain, so he played on the left-wing position in midfield, taking over from Ajax player Piet Keizer. He missed one game in the tournament (when Keizer played instead) and was only half-fit for the final after picking up an injury during the semi-final against Brazil. Rinus Michels gambled on Rensenbrink's fitness and played him from start – however he only lasted until half-time and was replaced by René van de Kerkhof. The Netherlands took an early lead through a Johan Neeskens penalty, but goals from Paul Breitner and Gerd Müller gave West Germany a 2–1 victory
. Rensenbrink's performances saw him named to the team of the tournament and he was sought by Ajax as a replacement for Keizer. However, contract negotiations fell through and he remained at Anderlecht.
In the 1978 FIFA World Cup tournament in Argentina, the Netherlands again reached the final, but this time without Cruijff (who decided to retire from international football) and under the guidance of Ernst Happel rather than Michels. Out of the shadow of Cruijff, Rensenbrink found more room to showcase his own considerable talent, playing on the left-hand side of a front three alongside Johnny Rep and René van de Kerkhof. He scored a hat-trick in the opening game against Iran, another goal against Scotland which was goal number 1000 in World Cup history and a penalty in the 5–1 win over Austria. In the final against Argentina, the Netherlands yet again met the hosts. In an intense match, the Netherlands fell behind to a first-half Mario Kempes strike. After Dick Nanninga's equalizer 9 minutes from time, a long pass from the Dutch captain Ruud Krol in the last 30 seconds of normal time gave Rensenbrink a half-chance to score but his shot from a very narrow angle was deflected on to the post and bounced clear
. Had he scored, it is almost certain that Holland would have won the World Cup with Rensenbrink being top goal scorer with Mario Kempes. Argentina scored twice in extra-time for a 3–1 victory and the Netherlands again had to settle for the runners-up spot.
Rensenbrink played some of the qualifiers for Euro 80, but after earning his 46th cap in 1979 (a 2–0 defeat by Poland in a qualifier for Euro 80), he retired from international football at the age of 32, having scored 14 times for his country. He along with Eusébio are the only players to score the most goals from a penalty spot in a tournament (4 in 1978).

He was named by Pelé as one of the top 125 greatest living footballers in March 2004. He was also named Anderlecht's greatest ever foreign player in 2008.

Personal life
Rensenbrink was married and lived in Oostzaan. In the summer of 2015, he revealed that he had been diagnosed with progressive muscular atrophy three years earlier. He died on 24 January 2020. Belgian news sources reported that he had been diagnosed with a muscular disease in 2012 which led to his death.

Career statistics

Club

International

Honours 

Club Brugge
Belgian Cup: 1969–70
Anderlecht
Belgian First Division: 1971–72, 1973–74
Belgian Cup: 1971–72, 1972–73, 1974–75, 1975–76
Belgian League Cup: 1973, 1974
European Cup Winners' Cup: 1975–76, 1977–78; runner-up: 1976–77
Amsterdam Tournament: 1976
European Super Cup: 1976, 1978
Tournoi de Paris: 1977
Jules Pappaert Cup: 1977
Belgian Sports Merit Award: 1978

Toulouse
Division 2: 1981–82

Netherlands
FIFA World Cup: runner-up 1974, 1978
UEFA European Football Championship: third place 1976
Individual
Belgian First Division top scorer: 1972–73
FIFA World Cup All-Star Team: 1974, 1978
European Cup Winners' Cup top scorer: 1975–76
IOC European Footballer of the Season: 1975–76
Belgian Golden Shoe: 1976
Onze d'Or: 1976
Ballon d'Or: runner-up 1976, third place 1978
Onze de Onze: 1976, 1977, 1978, 1979
FIFA World Cup Bronze Boot: 1978
FIFA World Cup Most Assists: 1978
Onze de Bronze: 1978, 1979
France Football's World Cup Top-100 1930-1990 46th: 1994
Planète Foot's 50 of the World's Best Players: 1996
FIFA 100: 2004
Placar's 100 World Cup Stars 42nd: 2005
Best foreign player in the Belgian First Division of all time: 2007
Best RSC Anderlecht player of all time: 2008
The Best Golden Shoe Team: 2011
Scorer of the 1000th World Cup goal
DH The Best RSC Anderlecht Team Ever: 2020

References

Other websites 

 Portland Timbers stats
 

1947 births
2020 deaths
Footballers from Amsterdam
Association football forwards
1974 FIFA World Cup players
1978 FIFA World Cup players
Luton Shelton (11 November 1985 – 22 January 2021) was a Jamaican footballer. He played as a striker or winger. He made his international debut for Jamaica in 2004.

In 2018, it was announced that Shelton has been diagnosed with ALS. He died from problems caused by the disease on 22 January 2021, aged 35.

References

Other websites
Profile  at SUFC.premiumtv.co.uk
AaB profile 

1985 births
2021 deaths
Deaths from motor neurone disease
Jamaican footballers
Paul Shrubb (1 August 1955 – 28 May 2020) was an English professional footballer, coach and scout. He made 350 appearances as a player in the Football League. He played for Brentford and Aldershot. 

He later returned to Aldershot as assistant manager and coached at a number of non-league clubs.

Shrubb was diagnosed with motor neurone disease in January 2006 and was given two years to live by doctors. He died from the disease on 28 May 2020, aged 64.

References

1955 births
2020 deaths
Deaths from motor neurone disease
English footballers
English football managers
Archie Yates (born 22 February 2009) is a British actor. He is known for winning a Critics' Choice Movie Award.

References 

2009 births
Living people
British child actors
Baintha Brakk is a  mountain in the Karakoram range, in Pakistan. It is also known as The Ogre. Baintha Brakk is part of the Panmah Muztagh subrange. It is the 85th highest mountain in the world.

The first people to reach the top were Chris Bonington and Doug Scott, in 1977. As of 2013, people had reached the top only three times.

References 

Mountains of Gilgit-Baltistan
Karakoram
In mathematics, the harmonic series is the divergent infinite series:

 

Divergent means that as you add more terms the sum never stops getting bigger. It does not go towards a single finite value.

Infinite means that you can always add another term. There is no final term to the series.

Its name comes from the idea of harmonics in music: the wavelengths of the overtones of a vibrating string are , , , etc., of the string's fundamental wavelength. Apart from the first term, every term of the series is the harmonic mean of the terms either side of it. The phrase harmonic mean also comes from music.

History
The fact that the harmonic series diverges was first proven in the 14th century by Nicole Oresme, but was forgotten. Proofs were given in the 17th century by Pietro Mengoli, Johann Bernoulli, and Jacob Bernoulli.
Harmonic sequences have been used by architects. In the Baroque period architects used them in the proportions of floor plans, elevations, and in the relationships between architectural details of churches and palaces.

Divergence

There are several well-known proofs of the divergence of the harmonic series. A few of them are given below.

Comparison test
One way to prove divergence is to compare the harmonic series with another divergent series, where each denominator is replaced with the next-largest power of two:

Each term of the harmonic series is greater than or equal to the corresponding term of the second series, and therefore the sum of the harmonic series must be greater than or equal to the sum of the second series.  However, the sum of the second series is infinite:

It follows (by the comparison test) that the sum of the harmonic series must be infinite as well.  More precisely, the comparison above proves that

for every positive integer .
This proof, proposed by Nicole Oresme in around 1350, is considered to be a high point of medieval mathematics. It is still a standard proof taught in mathematics classes today.

Integral test

It is possible to prove that the harmonic series diverges by comparing its sum with an improper integral.  Consider the arrangement of rectangles shown in the figure to the right. Each rectangle is 1 unit wide and  units high, so the total area of the infinite number of rectangles is the sum of the harmonic series:

The total area under the curve  from 1 to infinity is given by a divergent improper integral:

Since this area is entirely contained within the rectangles, the total area of the rectangles must be infinite as well. This proves that

The generalization of this argument is known as the integral test.
Rate of divergence
The harmonic series diverges very slowly. For example, the sum of the first 1043 terms is less than 100. This is because the partial sums of the series have logarithmic growth. In particular,

where  is the Euler–Mascheroni constant and  which approaches 0 as  goes to infinity. Leonhard Euler proved both this and also that the sum which includes only the reciprocals of primes also diverges, that is:

Partial sums

The finite partial sums of the diverging harmonic series,

 

are called harmonic numbers.

The difference between  and  converges to the Euler–Mascheroni constant. The difference between any two harmonic numbers is never an integer. No harmonic numbers are integers, except for .

Related series

Alternating harmonic series

The series

 

is known as the alternating harmonic series.  This series converges by the alternating series test.  In particular, the sum is equal to the natural logarithm of 2:
The alternating harmonic series, while conditionally convergent, is not absolutely convergent: if the terms in the series are systematically rearranged, in general the sum becomes different and, dependent on the rearrangement, possibly even infinite.

The alternating harmonic series formula is a special case of the Mercator series, the Taylor series for the natural logarithm.

A related series can be derived from the Taylor series for the arctangent:

 

This is known as the Leibniz series.

General harmonic series

The general harmonic series is of the form

where  and  are real numbers, and  is not zero or a negative integer.

By the limit comparison test with the harmonic series, all general harmonic series also diverge.

-series

A generalization of the harmonic series is the -series (or hyperharmonic series), defined as
for any real number . When , the -series is the harmonic series, which diverges. Either the integral test or the Cauchy condensation test shows that the -series converges for all  (in which case it is called the over-harmonic series) and diverges for all . If  then the sum of the -series is , i.e., the Riemann zeta function evaluated at .

The problem of finding the sum for  is called the Basel problem; Leonhard Euler showed it is . The value of the sum for  is called Apéry's constant, since Roger Apéry proved that it is an irrational number.

ln-series

Related to the -series is the ln-series, defined as

for any positive real number . This can be shown by the integral test to diverge for  but converge for all .

-series

For any convex, real-valued function  such that

the series

is convergent.

Random harmonic series

The random harmonic series
where the  are independent, identically distributed random variables taking the values +1 and −1 with equal probability , is a well-known example in probability theory for a series of random variables that converges with probability 1. The fact of this convergence is an easy consequence of either the Kolmogorov three-series theorem or of the closely related Kolmogorov maximal inequality. Byron Schmuland of the University of Alberta further examined the properties of the random harmonic series, and showed that the convergent series is a random variable with some interesting properties.  In particular, the probability density function of this random variable evaluated at +2 or at −2 takes on the value ..., differing from  by less than 10−42. Schmuland's paper explains why this probability is so close to, but not exactly, .  The exact value of this probability is given by the infinite cosine product integral  divided by .

Depleted harmonic series
The depleted harmonic series where all of the terms in which the digit 9 appears anywhere in the denominator are removed can be shown to converge and its value is less than 80.  In fact, when all the terms containing any particular string of digits (in any base) are removed the series converges.

Applications
The harmonic series can be counterintuitive. This is because it is a divergent series even though the terms of the series get smaller and go towards zero.  The divergence of the harmonic series is the source of some paradoxes. 

 The "worm on the rubber band". Suppose that a worm crawls along an infinitely-elastic one-meter rubber band at the same time as the rubber band is uniformly stretched. If the worm travels 1 centimeter per minute and the band stretches 1 meter per minute, will the worm ever reach the end of the rubber band? The answer, counterintuitively, is "yes", for after  minutes, the ratio of the distance travelled by the worm to the total length of the rubber band is
Because the series gets arbitrarily large as  becomes larger, eventually this ratio must exceed 1, which implies that the worm reaches the end of the rubber band. However, the value of  at which this occurs must be extremely large: approximately , a number exceeding 1043 minutes (1037 years). Although the harmonic series does diverge, it does so very slowly.

 The Jeep problem asks how much total fuel is required for a car with a limited fuel-carrying capacity to cross a desert leaving fuel drops along the route. The distance the car can go with a given amount of fuel is related to the partial sums of the harmonic series, which grow logarithmically.  And so the fuel required increases exponentially with the desired distance.
The block-stacking problem: given a collection of identical dominoes, it is possible to stack them at the edge of a table so that they hang over the edge of the table without falling. The counterintuitive result is that they can be stacked in a way that makes the overhang as large as you want. That is, provided there are enough dominoes.

  A swimmer that goes faster each time they touch the wall of the pool. The swimmer starts crossing a 10-meter pool at a speed of 2 m/s, and with every crossing, another 2 m/s is added to the speed. In theory, the swimmer's speed is unlimited, but the number of pool crosses needed to get to that speed becomes very large; for instance, to get to the speed of light (ignoring special relativity), the swimmer needs to cross the pool 150 million times. Contrary to this large number, the time needed to reach a given speed depends on the sum of the series at any given number of pool crosses:
Calculating the sum shows that the time required to get to the speed of light is only 97 seconds.

Related pages
 Harmonic progression
 List of sums of reciprocals

References

Other websites

 
 
 
 

Calculus
Sequences and series
Au is a municipality in Rheintal in the canton of St. Gallen in Switzerland.

References

Other websites 

  
 
 

Municipalities in Rheintal
Balgach is a municipality in Rheintal in the canton of St. Gallen in Switzerland.

References

Other websites 

 Official website 

Municipalities in Rheintal
Oberriet is a municipality in Rheintal in the canton of St. Gallen in Switzerland.

References

Other websites 

 Official website 

Municipalities in Rheintal
Diepoldsau is a municipality in Rheintal in the canton of St. Gallen in Switzerland.

References

Other websites 

 Official website 

Municipalities in Rheintal
Dublin is a city in the U.S. state of Texas.

Cities in Texas
Lott is a city in the U.S. state of Texas.

Cities in Texas
Rüthi is a municipality in Rheintal in the canton of St. Gallen in Switzerland.

References

Other websites 

 Official website 

Municipalities in Rheintal
New England or New England North West is the name given to a generally undefined region in the north of the state of New South Wales, Australia. It is about  inland, that includes the Northern Tablelands (or New England Tablelands) and the North West Slopes regions.

References

Other websites 

New South Wales Forecast Areas Map

Regions of New South Wales
Ronda is a town in Wilkes County, North Carolina, United States. The population was 417 at the 2010 census.

References

Towns in North Carolina
Wilkes County is a county located in the US state of North Carolina. As of the 2010 census, the population was 69,340.  Its county seat is Wilkesboro.

References

1770s establishments in North Carolina
1778 establishments in the United States
North Carolina counties
Wilkesboro is a town in and the county seat of Wilkes County, North Carolina. The population was 3,413 at the 2010 census.

References

Towns in North Carolina
County seats in North Carolina
Dmitri Yuryevich Chesnokov (; 26 April 1973 – December 2019) was a Russian professional footballer. He made his debut in the Russian Premier League in 1999 for FC Saturn Ramenskoye.

Chesnokov died in December 2019 at the age of 49.

References

Other websites
  Profile at Footballfacts

1973 births
2019 deaths
Russian footballers
Ward Swift Just (September 5, 1935 – December 19, 2019) was an American writer. He was a war correspondent and the author of 17 novels and many short stories. He was born in Michigan City, Indiana. Benjamin Bradlee hired Just at The Washington Post as a war correspondent for the Vietnam war. His novel An Unfinished Season was a finalist for the Pulitzer Prize for Fiction in 2005. His novel Echo House was a finalist for the National Book Award in 1997.

Just died on December 19, 2019 in Plymouth, Massachusetts of problems caused by Lewy body dementia, aged 84.

References

Other websites

Houghton Mifflin author page for Ward Just 
Perseus Books Group author page for Ward Just 
Ward Just resources on the Web 
Ward Just's Washington  by Michael Nelson, published in The Virginia Quarterly Review
1935 births
2019 deaths
Deaths from dementia with Lewy bodies
American novelists
American journalists
American political commentators
Writers from Indiana
Writers from Illinois
People from Michigan City, Indiana
People from Waukegan, Illinois
Sir Fazle Hasan Abed KCMG (27 April 1936 – 20 December 2019) was a Bangladeshi businessman. He was the founder and Chair Emeritus of BRAC. This was one of the world's largest non-governmental organizations.

Abed died on 20 December 2019 at a Dhaka hospital from respiratory failure caused by glioblastoma, aged 83.

References

1936 births
2019 deaths
People from Sylhet Division‎
Bangladeshi businesspeople
Order of St Michael and St George
Eduard "Eddie" Franz Krieger (16 December 1946 – 20 December 2019) was an international Austrian footballer.

Krieger started his professional career at Austria Wien. After a play at Dutch side VVV-Venlo, Krieger returned to Austria to finish his career at LASK Linz. He made his debut for Austria in April 1970 and was a participant at the 1978 FIFA World Cup. He earned 25 caps, no goals scored. He played his final international match in 1978.

References

Other websites
 Profile - Weltfussball 
 Profile - Club Brugge
 Profile  - Austria Archive

1946 births
2019 deaths
Sportspeople from Vienna
Austrian footballers
Players of LASK
Yuri Pavlovich Pshenichnikov (Russian: Юрий Павлович Пшеничников; 2 June 1940 – 20 December 2019)  was an Uzbek-born Soviet-Russian football goalkeeper and coach. He was born in Tashkent. He earned 19 caps for the USSR national football team, and participated in UEFA Euro 1968.

Pshenichnikov died on 20 December 2019 in Moscow at the age of 79.

References

Other websites
Profile (in Russian) 

1940 births
2019 deaths
Uzbekistani footballers
Soviet footballers
D. Selvaraj (; 14 January 1938 – 20 December 2019) was a Tamil writer. He was the author of a number of novels, short stories, and plays in Tamil. He received the Tamil Nadu Government's literary award for the best Novel for 2011 for his work on tannery workers of Southern Tamil Nadu titled "Thol". He also won the Sahitya Akademi award for Tamil in 2012.

Selvaraj died on 20 December 2019 from an illness at a private hospital in Chennai at the age of 81.

Works
 Malarum charugum (Novel) (Malligai, 1967)
 Theneer (Novel) (New Century book house, 1973)
 Moolathanam (Novel) (1977)
 Agnikundam (Novel) (1980)
 Yugasangamam (Play) (1968)
 Jeeva - Biography of P Jeevanandham (Sahitya Akademi, 2005)
 Saamichidambaranaar - Biography of Tamil writers (Sahitya Akademi, 2006).
 Pradosham (Varam:Chennai, 2007)
 Thole (2010) - Awarded best novel of the year by the Tamil Nadu Government - Presented by the Hon Chief Minister Dr. J. Jayalalithaa on April 13, 2012

References
References

2019 deaths
1938 births
Disease-related deaths in India
Indian writers
Preity G Zinta (pronounced ; born 31 January 1975) is an Indian actress and businesswoman. Her first movie roles were in Dil Se.. in 1998, followed by a role in Soldier in the same year.

She is known for her role as a teenage single mother in Kya Kehna (2000). She also got a lot of credit for her roles in films such as  Chori Chori Chupke Chupke (2001), Dil Chahta Hai (2001), Dil Hai Tumhaara (2002), and Armaan (2003), and she especially won the Filmfare Award for Best Actress for her performance in the drama Kal Ho Naa Ho (2003). She also played leading roles in the science fiction film Koi... Mil Gaya (2003) and the romantic drama Veer-Zaara (2004), which were the two consecutive top-grossing films in India for her. She also played other roles like a modern Indian woman in both Salaam Namaste (2005) and Kabhi Alvida Naa Kehna (2006), which were the highest grossing productions in the overseas markets.

References
References

1975 births
Living people
Indian movie actors
Indian television actors
Indian businesspeople
Indian movie producers
Thomas Chandy (29 October 1947 – 20 December 2019) was an Indian businessman and politician. He was born in Chennamkary, Kerala, India. Chandy was a member of the Kerala Legislative Assembly from 2006 until his death. In 2017, he was the Minister of Transport of Kerala. Chandy was a member of the Nationalist Congress Party.

Chandy died of stomach cancer at a hospital in Ernakulam, Kerala on 20 December 2019 at the age of 72.

References

1947 births
2019 deaths
Politicians from Kerala
Indian businesspeople
Charles Ingerham “Chuck” Peddle (November 25, 1937 – December 15, 2019) was an American electrical engineer. He was born in Bangor, Maine. He was best known as the main designer of the MOS Technology 6502 microprocessor, as well as the KIM-1 SBC (single-board computer) and the Commodore PET PC (personal computer).

Peddle died at the age of 82 on December 15, 2019 at his Santa Cruz, California home of pancreatic cancer.

References

Other websites
 The Legendary Chuck Peddle, Inventor of The Personal Computer
 Chuck Peddle tells his story on The Amp Hour Podcast

1937 births
2019 deaths
Deaths from pancreatic cancer
Cancer deaths in California
Engineers from Maine
American inventors
Scientists from Maine
People from Bangor, Maine
Andriy Mykhailovych Danylko (; ; born 2 October 1973), better known for his drag stage name Verka Serduchka (; ), is a Ukrainian comedian, actor and pop and dance singer. 

Danylko represented Ukraine in the Eurovision Song Contest 2007 and finished in second place.

Interesting Facts 
In November 2022, Andriy Danylko put up for auction at Sotheby's the previously purchased Rolls-Royce Silver Shadow 1974, which belonged to Freddie Mercury. On November 5, 2022, the car was sold at an auction for 250,000 pounds (11 million hryvnias). All 100% of the proceeds were directed by Andriy Danylko to the construction of a new modern center for the rehabilitation and prosthetics of Ukrainians injured in the war in the Lviv region.

References

Other websites
 Official website
 Official video channel on YouTube

1973 births
Drag queens
Eurovision Song Contest entrants
Living people
Ukrainian comedians
Ukrainian singers
Ukrainian actors
Pop singers
Folk singers
Carlos Fernando Rosenkrantz (born 27 October 1958) is an Argentine lawyer. He is a member of the Supreme Court of Argentina since August 2016, nominated by president Mauricio Macri's. He served as president of the court from October 2018 to 2021, currently serves as vice president of the court.

Biography
Rosenkrantz was born in Buenos Aires. His father was a Jewish-Polish immigrant and his mother a teacher from Corrientes Province. 

He studied law at the University of Buenos Aires and later in the United States thanks a Fulbright Scholarship.

References 

1958 births
Politicians from Buenos Aires
Living people
Argentine lawyers
Argentine judges
Sergio Tomás Massa (born 28 April 1972) is an Argentine politician who is a candidate for President of Argentina in the 2023 election. He became the country's Minister of Economy on 2 August, 2022. He was the president of the Argentine Chamber of Deputies from 2019 until 2022. He was also a national deputy for Buenos Aires Province. 

Massa is the founder and current leader of the peronist Renewal Front. He was Chief of the Cabinet of Ministers from 2008 to 2009 under Cristina Fernández de Kirchner.

1972 births
Living people
Presidents of the Argentine Chamber of Deputies
Winamac is a town in the Monroe Township in Pulaski County in the state of Indiana, in the United States. It is the county seat of Pulaski County. As of the 2010 census, 2,490 people lived in Winamac.

References 

Towns in Indiana
County seats in Indiana
The Karate Kid Part III is a 1989 American martial arts drama movie and the second sequel to The Karate Kid (1984). The movie stars Ralph Macchio, Pat Morita, Robyn Lively, and Thomas Ian Griffith in his movie debut. As was the case with the first two movies in the series, it was directed by John G. Avildsen and written by Robert Mark Kamen, with stunts choreographed by Pat E. Johnson and the music composed by Bill Conti. In the movie, the returning John Kreese, with the help of his best friend Terry Silver, tries to get revenge on Daniel LaRusso and Mr. Miyagi which involves hiring a ruthless martial artist and harming their relationship.

Cast 
 Ralph Macchio as Daniel LaRusso
 Noriyuki "Pat" Morita as Mister Miyagi
 Robyn Lively as Jessica Andrews
 Thomas Ian Griffith as Terry Silver
 Martin Kove as John Kreese
 Sean Kanan as Mike Barnes
 Randee Heller as Lucille LaRusso
 Jonathan Avildsen as Snake
 Christopher Paul Ford as Dennis
1989 movies
1980s sequel movies
American sequel movies
1980s English-language movies
Karate movies
Movies directed by John G. Avildsen
Versailles is a town in the state of Indiana, in the United States.

Towns in Indiana
County seats in Indiana
Nashville is a town in the state of Indiana, in the United States.

Towns in Indiana
County seats in Indiana
Rebstein is a municipality in Rheintal in the canton of St. Gallen in Switzerland.

References

Other websites 

 Official website 

Municipalities in Rheintal
Berneck is a municipality in Rheintal in the canton of St. Gallen in Switzerland.

References

Other websites 

 Gemeinde Berneck Official website 

Municipalities in Rheintal
Eichberg is a municipality in Rheintal in the canton of St. Gallen in Switzerland.

References

Other websites 

 Official website 

Municipalities in Rheintal
Tübach is a municipality in Rorschach in the canton of St. Gallen in Switzerland.

References

Other websites 

 Official website 

Municipalities in Rorschach
Rockville is a town in the state of Indiana, in the United States.

Towns in Indiana
County seats in Indiana
Fort Branch is a town in the state of Indiana, in the United States.

Towns in Indiana
Hazleton is a town in the state of Indiana, in the United States.

Towns in Indiana
Gurnard is a village and civil parish  on the Isle of Wight, two miles to the west of Cowes. Gurnard sits on the edge of Gurnard Bay, used by the Gurnard Sailing Club.

Gurnard's main street features a pub (Portland Inn), Doughty Newnham Chartered Surveyors office (a company of measurers and mapmakers), a few shops, and a few houses. The west end of the beach is called Gurnard Marsh and there is a stream called "The Luck" flows into the Solent. 

A fort known as Gurnard Fort was built on a coastal high point west of Gurnard Marsh about 1600. The land washed away into the ocean, however, and the remains of the fort were lost and forgotten until a nearby Roman home was dug up in 1864, when the fort was found.

Transport is provided by the former Wightbus route 32 to and from Cowes, now run by Southern Vectis. There is no longer a direct service to Newport, Isle of Wight.

References

Other websites
Other websites

Gurnard Sailing Club website
Isle of Wight Council information
Doughty Newnham Chartered Surveyors website
Photos, accommodation guide, hotels and tourist  information

Villages on the Isle of Wight
Streetman is a town in the U.S. state of Texas.

References 

Towns in Texas
Fluminense de Feira Futebol Clube, usually known as Fluminense de Feira, or just Fluminense are a Brazilian football team from Feira de Santana, Bahia, Brazil, founded on January 1, 1941.

Games are played in the Joia da Princesa stadium, capacity 16,274. The team plays in white, red and green striped shirts, white shorts and white socks.

History
On January 1, 1941, Fluminense de Feira Futebol Clube was founded. Fluminense de Feira became a professional team in 1954. Two years later, the club was runner-up in Campeonato Baiano. In 1963, the club won Campeonato Baiano, its first professional title. In 1968, the club was again Campeonato Baiano runner-up. In the following year, the club won again the state championship.

In 1992, Fluminense de Feira was runner-up of Brazilian Third Division, after losing the final to Tuna Luso. But, no promotion was given to Fluminense de Feira or Tuna Luso, because neither the second division, nor the third division were disputed in 1993.