【数学】(1-1/2²)(1-1/3²)(1-1/4²)(1-1/5²)……

问题描述:

【数学】(1-1/2²)(1-1/3²)(1-1/4²)(1-1/5²)……
(1-1/2²)(1-1/3²)(1-1/4²)(1-1/5²)……(1-1/99²)(1-1/100²)

用平方差
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/100)(1+1/100)
=(1/2)(3/2)(2/3)(4/3)……(99/10)(101/10)
中间约分
=(1/2)(101/100)
=101/200