Question

(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)........+(1+1/99

求简便算法，最后的括号没打完整，但还是有的
答得好还可以加悬赏

Answer 1

答：
(1+1/2)×(1-1/2)×(1+1/3)×(1-1/3)×.....×(1+1/99)
=(1+1/2)×(1+1/3)×....×(1+1/99)×(1-1/2)×(1-1/3)×....×(1-1/98)
=(3/2)×(4/3)×(5/4)×....×(100/99) ×(1/2)×(2/3)×(3/4)×....×(97/98)
=(100/2)×(1/98)
=50/98
=25/49
中间采用了错位相消法....