1*3,2*4,3*5,...n(n+2)求数列的前n项和Sn的详细步骤,最好有,每一步,答案是n(n+1)(2n+7)/6

问题描述:

1*3,2*4,3*5,...n(n+2)求数列的前n项和Sn的详细步骤,最好有,每一步,答案是n(n+1)(2n+7)/6

原式=1×(1+2)+2×(2+2)+3×(3+2)+……+n(n+2)
=1²+2²+3²+……+n²+2×(1+2+3+……+n)
=1/6×n(n+1)(2n+1)+n(n+1)
=1/6n(n+1)(2n+7)