Question

1乘2十2乘3十3乘4十…n乘(n十1)

Answer 1

1x2+2x3+3x4+······+n(n+1)=1x(1+1)+2x(2+1)+3x(3+1)+········+n(n+1)=1^2+1+2^2+2+3^2+3+·······+n^2+n=(1^2+2^2+3^2+·········+n^2)+(1+2+3+········+n)=n(n+1)(2n+1)/6+n(...