(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/9²)(1/10²)=?

问题描述:

(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/9²)(1/10²)=?

1-1/2²=1-(1/2)²=1²-(1/2)²=(1+1/2)(1-1/2) (最后一步平方差得来的)
每一项都可以这样拆
所以,原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/10)(1+1/10)
=(1/2)(3/2)(2/3)(4/3)……(9/10)(11/10)
约分后只剩一头一尾了
=(1/2)(11/10)
=11/20
完毕!