Question

1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6+1/5*6*7

为多少？
我要的是通法。

Answer 1

原式=（1/1*2-1/2*3+1/2*3-……+1/5*6-1/6*7）*1/2
=（1/1*2-1/6*7）*1/2
=10/21*1/2
=5/21
1/n(n+1)(n+2)=[1/n(n+1)-1/(n+1)(n+2)]*1/2
100%正确！！！！
相信我吧！！

Answer 2

1/n(n+1)(n+2)=[1/n(n+1)-1/(n+1)(n+2)]/2
1/1x2x3 + 1/2x3x4 +1/3x4x5 + … + 1/n(n+1)(n+2)
=[∑1/n(n+1)-∑1/(n+1)(n+2)]/2
=[1-1/(n+1)-1/2+1/(n+2)]/2
=1/4-1/(2(n+1)(n+2))