用平方差公式
(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/99^2)(1-1/100^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/99)(1+1/99)(1-1/100)(1+1/100)
=(1/2)(3/2)(2/3)(4/3)……(98/99)(100/99)(99/100)(101/100)
=(1/2)(101/100)
=101/200
用平方差公式
(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/99^2)(1-1/100^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/99)(1+1/99)(1-1/100)(1+1/100)
=(1/2)(3/2)(2/3)(4/3)……(98/99)(100/99)(99/100)(101/100)
=(1/2)(101/100)
=101/200