计算3x(1x2+2x3+3x4+……+99x100)的值是A97x98x99 B98x99x100 C99x100x101D100x101x102
问题描述：
计算3x(1x2+2x3+3x4+……+99x100)的值是A97x98x99 B98x99x100 C99x100x101D100x101x102
答
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
3x(1x2+2x3+3x4+……+99x100)=3X99X100X202/6=99x100x101
选C