计算:(1-1/2²)(1-1/3²)(1-1/4²)x...x(1-1/19²)(1-1/20²)

问题描述:

计算:(1-1/2²)(1-1/3²)(1-1/4²)x...x(1-1/19²)(1-1/20²)

平方差
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/20)(1+1/20)
=(1/2)(3/2)(2/3)(4/3)……(19/20)(21/20)
中间约分
=(1/2)(21/20)
=21/40