证明1x2+2x3+…+n(n+1)=n(n+1)(n+2)/31x2+2x3+…+n(n+1)=1x(1+1)+2x(2+1)+.+n(n+1)=(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证明1x2+2x3+…+n(n+1)（n+2）=n(n+1)(n+2)(n+3)/4是错的,我...