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