総和
∑ i = 1 n 0 = 0 {\displaystyle \textstyle \sum \limits _{i=1}^{n}0=0}
∑ i = 1 n 1 = n {\displaystyle \textstyle \sum \limits _{i=1}^{n}1=n}
∑ i = 1 n C = n C {\displaystyle \textstyle \sum \limits _{i=1}^{n}C=nC}
∑ i = 1 n i = 1 2 n ( n + 1 ) {\displaystyle \textstyle \sum \limits _{i=1}^{n}i={\dfrac {1}{2}}{n(n+1)}}
∑ i = 1 n i 2 = 1 6 n ( n + 1 ) ( 2 n + 1 ) {\displaystyle \textstyle \sum \limits _{i=1}^{n}i^{2}={\dfrac {1}{6}}{n(n+1)(2n+1)}}
∑ i = 1 n i 3 = { 1 2 n ( n + 1 ) } 2 {\displaystyle \textstyle \sum \limits _{i=1}^{n}i^{3}=\left\{{\dfrac {1}{2}}n(n+1)\right\}^{2}}
∑ i = 1 n i 4 = 1 30 n ( n + 1 ) ( 2 n + 1 ) ( 3 n 2 + 3 n − 1 ) {\displaystyle \textstyle \sum \limits _{i=1}^{n}i^{4}={\dfrac {1}{30}}n(n+1)(2n+1)(3n^{2}+3n-1)}