「※」表示一種運算符號，它的定義是a※b＝ab/（a＋b），求 1/【1/（1※2）－1/（2※3）＋1/（3※4）－1/（4※5）＋……－1/（100※101）】之值?

a※b＝ab/(a＋b) 

=> 1/(a※b) = (a+b)/ab = (1/b)+(1/a) = (1/a)+(1/b)1/(1※2) - 1/(2※3) + 1/(3※4) - 1/(4※5) +…-1/(100※101)= (1/1)+(1/2) -(1/2)-(1/3) + (1/3)+(1/4) -(1/4)-(1/5) + ...

　-(1/100)-(1/101)

= (1/1) -(1/101)

= 1 -(1/101)

= 100/101

∴ 1/ 【1/(1※2) - 1/(2※3) + 1/(3※4) - 1/(4※5) +…-1/(100※101)】

= 1/ (100/101)

= 101/100