(1-1/2²)(1-1/3²)(1-1/4²)...(1-1/99²)(1-1/100²)=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)....(1-1/99)(1+199)(1-1/100)(1+1/100)=1/2*3/2*2/3*4/3*3/4*5/4*.....98/99*100/99*99/100*101/100=1/2*101/100=101/200
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