1/1*2+1/2*3+1/3*4+……+1/19*20+1/20*21的答案,

问题描述:

1/1*2+1/2*3+1/3*4+……+1/19*20+1/20*21的答案,

1/(1*2) = 1- 1/2
1/(2*3) = 1/2 - 1/3
依次类推
原式= 1 - 1/2 + 1/2 - 1/3 +...+ 1/20 - 1/21
= 1 - 1/21
= 20/21