(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