(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/100²)

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(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/100²)(1-1/2²)(1-1/3²)(1-1/4²)……(1-

(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/100²)
(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/100²)

(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/100²)
(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)……(1-1/100)(1+1/100)
=1/2×3/2×2/3×4/3×3/4×……99/100×101/100
=1/2×101/100
=101/200