1+(n+2)+(2n+3)+(3n+4)+(4n+5)+……((n-1)n+n)的答案

来源：学生作业帮助网编辑：作业帮时间：2024/04/29 03:31:47

1+(n+2)+(2n+3)+(3n+4)+(4n+5)+……((n-1)n+n)的答案
1+(n+2)+(2n+3)+(3n+4)+(4n+5)+……((n-1)n+n)的答案

1+(n+2)+(2n+3)+(3n+4)+(4n+5)+……((n-1)n+n)的答案
1+(n+2)+(2n+3)+(3n+4)+(4n+5)+……((n-1)n+n)
=(1+2+3+...+n)+(n+2n+3n+.(n-1)n)
=(1+n)n/2+n(1+2+3+.(n-1))
=(1+n)n/2+n*(1+n-1)(n-1)/2
=(1+n)n/2+n^2(n-1)/2
=n/2(1+n+n^2-n)
=n(n^2+1)/2

(n*n*n+n)/2