1x2+2x3+3x4+...+n（n+1）=?

1x2+2x3+3x4+...+n（n+1）=1^2+1+2^2+2+3^2+3+...+n^2+n=1+2+...+n+(1^2+2^2+...+n^2)=(1+n)n/2+n(n+1)(2n+1)/6=n(n+1)/2*(1+(2n+1)/3)=n(n+1)(2n+5)/6---看通项,再分解,利用公式!