裂项相消,1/1*2+1/2*3..+1/19*20 写出过程

裂项相消,1/1*2+1/2*3..+1/19*20 写出过程
裂项相消,1/1*2+1/2*3..+1/19*20 写出过程

裂项相消,1/1*2+1/2*3..+1/19*20 写出过程
1/1*2+1/2*3..+1/19*20
=1-1/2+1/2-1/3+1/3-1/4+……+1/19-1/20
=1-1/20
=19/20

1/1*2+1/2*3.。。。。。+1/19*20
=(1/1 - 1/2) + (1/2-1/3) + (1/3-1/4) + ...... + (1/19 - 1/20)
=1-1/20
=19/20

1/n-1/n+1=1/n(n+1),可以验证下