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

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

アイデア:
(1/1*2)は(1-1/2)
(1/2*3)は(1-1/3)

依此推理
得:
=1-1/2+1/2-1/3…… +1/49-1/50
=1-1/50
=49/50