1/1*2 + 1/2*3 + 1/3*4 .+ 1/49*50=?

1/1*2 + 1/2*3 + 1/3*4 .+ 1/49*50=?
1/1*2 + 1/2*3 + 1/3*4 .+ 1/49*50=?

1/1*2 + 1/2*3 + 1/3*4 .+ 1/49*50=?
思路:
因为(1/1*2)就是(1-1/2)
(1/2*3)就是(1-1/3)
.
依此推理
得:
=1-1/2+1/2-1/3……+1/49-1/50
=1-1/50
=49/50

1/1*2+1/2*3+1/3*4......+1/49*50
=1/1*(1+1)+1/2*(2+1)+......+1/49*(49+1)
=1-50/1
=49/50

=1-1/2+1/2-1/3……+1/49-1/50
=1-1/50
=49/50

=1 - 1/2 + 1/2-1/3 + 1/3 - 1/4 + ....+ 1/(n-1) - 1/n
=1-1/n
=n-1 / n