(1-1/2²)(1-1/3²)(1-1/4²)........(1-1/n²)
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(1-1/2²)(1-1/3²)(1-1/4²)........(1-1/n²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)........(1-1/n)(1+1/n)
=1/2*3/2*2/3*4/3*3/4*5/4.............*(n-1)/n*(n+1)/n
=1/2*(n+1)/n
=(n+1)/2n
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)........(1-1/n)(1+1/n)
=1/2*3/2*2/3*4/3*3/4*5/4.............*(n-1)/n*(n+1)/n
=1/2*(n+1)/n
=(n+1)/2n
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(1-1/2²)(1-1/3²)(1-1/4²)........(1-1/n²)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)........(1+1/n)(1-1/n)
=3/2×4/3×5/4×……×(n+1)/n×1/2×2/3×3/4×……×(n-1)/n
=(n+1)/2×1/n
=(n+1)/2n
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)........(1+1/n)(1-1/n)
=3/2×4/3×5/4×……×(n+1)/n×1/2×2/3×3/4×……×(n-1)/n
=(n+1)/2×1/n
=(n+1)/2n
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