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

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

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

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

(1-1/4)(1-1/9)(1-1/16)(1-1/25)...(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)
=3/2*1/2*4/3*2/3*5/4*3/4*6/5*4/5..........100/99*98/99*101/100*99/100
=1/2*101/100
=101/200