求 $1^n+2^n+3^n+\cdots+k^n$
若记 $a_n(k)=1^n+2^n+3^n+\cdots+k^n$, 则熟知有
\[a_1(k)=1+2+3+\cdots+k=\frac{1}{2}k(k+1)\]
Answer
若记 $a_n(k)=1^n+2^n+3^n+\cdots+k^n$, 则熟知有
\[a_1(k)=1+2+3+\cdots+k=\frac{1}{2}k(k+1)\]