2021-07-20
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(1-1/2²)(1-1/3²)(1-1/4²)……(1-1/10²)
= (1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4) ....... (1-1/10)(1+1/10)
= (1/2)(3/2)(2/3)(4/3)(3/4)(5/4) ....... (9/10)(11/10)
= (1/2)(11/10)
= 11/20
= (1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4) ....... (1-1/10)(1+1/10)
= (1/2)(3/2)(2/3)(4/3)(3/4)(5/4) ....... (9/10)(11/10)
= (1/2)(11/10)
= 11/20
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