(1-1/2²)(1-1/3²)(1-1/4²)...(1-1/100²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/100)(1+1/100)
=(1/2)(3/2)(2/3)(4/3)(3/4)(5/4)(4/5).(100/99)(99/100)(101/100)
=(1/2)(101/100)
=101/50
用简便方法计算（因式分解的公式法）
(1-1/2²)(1-1/3²)(1-1/4²)...(1-1/100²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/100)(1+1/100)
=(1/2)(3/2)(2/3)(4/3)(3/4)(5/4)(4/5).(100/99)(99/100)(101/100)
=(1/2)(101/100)
=101/50