已知1∧2+2∧2+3∧2+…+n∧2=1/6*n*(n+1)(2n+1),则数列1*2,2*3,3*4,…,n(n+1)的前n项和为?

问题描述:

已知1∧2+2∧2+3∧2+…+n∧2=1/6*n*(n+1)(2n+1),则数列1*2,2*3,3*4,…,n(n+1)的前n项和为?
已知1∧2+2∧2+3∧2+…+n∧2=1/6*n*(n+1)(2n+1) 求数列1*2,2*3,3*4,…,n(n+1)的前n项和

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∧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) =1/3*n*(n+1)(n+2)