(1-1/4)×(1-1/9)×(1-1/16)×...×(1-1/10000)=(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)……(99/100)(101/100)=(1/2)*(101/100)=101/200中间项两两抵消了。
用平方差公式打开,然后约分,答案:101/200