1x2+2x3+3x4+4x5+.+n(n+1)等于多少?急救!
问题描述：
1x2+2x3+3x4+4x5+.+n(n+1)等于多少?急救!
请写下过程,谢谢
答
1x2+2x3+3x4+…+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) =1/6*n(n+1)(2n+1)+1/2*n(n+1) =1/6*n(n+1)(2n+1+3)(提取公因式） =1/3*n(n+1)(n+2)