用简便方法求值:(1-1/2²)(1-1/3²)(1-1/4²)...(1-1/99²)(1-1/100²)

问题描述:

用简便方法求值:(1-1/2²)(1-1/3²)(1-1/4²)...(1-1/99²)(1-1/100²)

原式=1*3/2^2* 2*4/3^2*..* 99*101/100^2
=101/(2*100)
=101/200