(1-1/4)(1-1/9)(1-1/16)(1-1/25)...(1-1/10000)_数学解答

(1-1/4)(1-1/9)(1-1/16)(1-1/25)...(1-1/10000)

人气：336 ℃　时间：2020-03-23 06:39:30

解答

原式
=(1-1/2)(1+1/2) * (1-1/3)(1+1/3) * ...* (1-1/100)(1+1/100) 平方差
=1/2 * 2/3 * 3/4 * ...* 99/100 * 3/2 * 4/3 * 5/4 * ...* 101/100 整理,抵消
=1/2 * 101/100
=101/200
=0.505