题目

求和：S(n)=n+2(n-1)+3(n-2)+...+n

提问时间：2021-01-15

答案

S(n)=n+2(n-1)+3(n-2)+...+n
=∑[k=1,n] (n+1-k)*k
=∑[k=1,n] k（n+1）-∑[k=1,n]k^2
=（n+1）∑[k=1,n] k-n(n+1)(2n+1)/6
=n（n+1）^2/2-n(n+1)(2n+1)/6
=n(n+1)(n+2)/6