Question

好难的数学题呀

观察；1x2=三分之一x(1x2x3-0x1x2)
思考：

1x2+2x3......+100x101=
1x2+2x3+......+n(n+1)=
1x2x3+2x3x4+......+n(n+1)(n+2)=

Answer 1

1x2+2x3......+100x101=(1²+2²+....+100²)+100
=100x(100+1)x(2x100+1)/6+100=.....
1x2+2x3+......+n(n+1)
=(1²+2²+....+n²)+n=n(n+1)x2n+1)/6 +n

1x2x3+2x3x4+......+n(n+1)(n+2)
=(1^3+2^3+....+n^3)+3(1²+2²+....+n²)+2(1+2+3+...+n)
=[n(n+1)/2]^2+n(n+1)(2n+1)/6 +n +n(n+1)
=......
剩下的自己动手算算吧！

Answer 2

这是什么意思，题目呢