一次方和:∑i=1ni=(n+1)(n)/2\sum_{i=1}^{n}i=(n+1)(n)/2∑i=1ni=(n+1)(n)/2
二次方和:∑i=1ni2=n(n+1)(2n+1)/6\sum_{i=1}^{n}i^2=n(n+1)(2n+1)/6∑i=1ni2=n(n+1)(2n+1)/6
三次方和:∑i=1ni3=n2(n+1)2/4\sum_{i=1}^{n}i^3=n^2(n+1)^2/4∑i=1ni3=n2(n+1)2/4
四次方和:∑i=1ni4=n(n+1)(2n+1)(3n2+3n−1)/30\sum_{i=1}^{n}i^4=n(n+1)(2n+1)(3n^2+3n-1)/30∑i=1ni4=n(n+1)(2n+1)(3n2+3n−1)/30