1x2+2x3+3x4+.99x100=?

题目

1x2+2x3+3x4+.99x100=?

答案

1x2+2x3+3x4+…+n(n+1)
=1x(1+1)+2x(2+1)+3x(3+1)+…n(n+1)
=(1^2+2^2+3^2+…+n^2)+(1+2+3+…+n)
=n(n+1)(2n+1)/6+n(n+1)/2
=n(n+1)[(2n+1)+3]/6
你令n=99,带入就可以了