1乘2 加 2乘3 加 3乘4 加.加n乘(n加1)等于几

网友回答

1*2+2*3+3*4+……+n(n+1) =(1^2+1)+(2^2+2)+(3^2+3)+……+(n^2+n) =(1^2+2^2+3^3+……+n^2)+(1+2+3+……+n) =n(n+1)(2n+1)/6+n(n+1)/2 =n(n+1)(n/3+1/6+1/2) =n(n+1)(n/3+2/3) =n(n+1)(n+2)/3
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