问题

数论 >> 一般数论 >> 初等数论
Questions in category: 初等数论 (Elementary Number Theory).

求 $1^n+2^n+3^n+\cdots+k^n$

Posted by haifeng on 2012-05-04 18:39:14 last update 2012-05-04 18:39:14 | Answers (0) | 收藏


若记 $a_n(k)=1^n+2^n+3^n+\cdots+k^n$, 则熟知有

\[a_1(k)=1+2+3+\cdots+k=\frac{1}{2}k(k+1)\]