(1-1/10²)(1-1/11²)...(1-1/99²)(1-1/100²)

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(1-1/10²)*(1-1/11²)*...*(1-1/99²)*(1-1/100²)(1-1/10²)*(1-1/11²)*...*(1

(1-1/10²)*(1-1/11²)*...*(1-1/99²)*(1-1/100²)
(1-1/10²)*(1-1/11²)*...*(1-1/99²)*(1-1/100²)

(1-1/10²)*(1-1/11²)*...*(1-1/99²)*(1-1/100²)
解；
原式=(1-1/10)(1+1/10)*(1-1/11)(1+1/11)*……*(1-1/100)(1+1/100)
=9/10*11/10*10/11*12/11*…………*99/100*101/100
=1/10*101/100
=101/1000