sn=1×3+2×5+3×7+...+n×(2n+1)数列求和
问题描述:
sn=1×3+2×5+3×7+...+n×(2n+1)数列求和
答
sn=1×3+2×5+3×7+...+n×(2n+1)
=(2×1^2+1)+(2×2^2+2)+……+(2×n^2+n)
=2×(1^2+2^2+……+n^2)+(1+2+……+n)
=n(n+1)(2n+1)/6+n(n+1)/2
=n(n+1)(n+2)/3