movie

Ram, Shyam, Ghanshyam are critics of movies. The have recently downloaded a
series of movies and are going to watch them. Ram claims that the movie of the 
entire series should be watched strictly in the same order as they are given, 
because there is a message given by the director in the movie’s order.

Shyam, being chaotic, does not think so, hence se loves watching movies in a 
random order. Shyam is good in convincing other people, so after a long 
discussion, Ram accepted watching in random order. In  this context random 
order means that there are N movies in the series. In the very beginning a 
random movie is chosen (Every movie has an equal probability to be chosen).

After the movie is over the next one is chosen randomly and independently of 
what have been watched before.
Ghanshyam is a student of a good university, he does not like movies but he 
wonders, what is the expected number of movies guys have to watch until 
every movie is watched atleast once.

The first line of input contains T denoting no. of test cases followed by T lines each containing an integer denoting total no. of movies N in the series.

1 ≤ T ≤ 1000
1 ≤ N ≤ 100000

SAMPLE INPUT
3
1
2
3

SAMPLE OUTPUT
1.0
3.0
5.5

Explanation

Case 2 - After watching the first movie there is ½ chance to finish the series each time new movie is
watched. 

So the expected number of movies is 2/2+3/4+4/8…=3

Source: hackerearth | Difficulty: EASY


Solutions: