Question

考考你,（1*2）+（2*3）+（3*4）+……前n项的和?

Answer 1

Sn

=1*2+2*3+.+n*(n+1)

=1/3*[(3-0)*1*2+(4-1)*2*3+.+(n+2-(n-1))*n*(n+1)]

=1/3*[-0*1*2+1*2*3-1*2*3+2*3*4-.-(n-1)*n*(n+1)+n*(n+1)*(n+2)]

=1/3*n*(n+1)(n+2)

=n*(n+1)(n+2)/3