(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/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/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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