1X2+2X3+3X4+.NX(N+1)

问题描述:

1X2+2X3+3X4+.NX(N+1)

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