从1乘以2分之1一直加到49乘以50分之1的得数是多少?

Question

从1乘以2分之1一直加到49乘以50分之1的得数是多少?

Answer 1

1/(1*2)+1/(2*3)+1/(3*4)+.+1/(49*50)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.+(1/49-1/50)
=1-1/2+1/2-1/3+1/3-1/4+.-1/49+1/49-1/50
=1+0+0+0+.-1/50
=1-1/50
=49/50
类似：1/[a*(a+n)]=(1/n)*[1/a-1/(a+n)]
例子：
1/56=1/(7*8)=1/7-1/8
1/12=1/(2*6)=(1/4)*[1/2-1/6]
.
等等