求和:Sn=1+2x3+3x5+……+nx(2n-1)
问题描述:
求和:Sn=1+2x3+3x5+……+nx(2n-1)
答
an=n(2n-1)=2n²-n
所以Sn=2(1²+2²+……+n²)-(1+2+……+n)
=2n(n+1)(2n+1)/6-n(n+1)/2
=n(n+1)(4n-1)/6