求连乘积 (1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)…(1+1/n)(1-1/n)

中国上海市

(1+1/2)(1－1/2)(1+1/3)(1－1/3)(1+1/4)(1－1/4)……(1+1/9999)(1－1/9999)……(1－1/n)(1+1/n)

波斯猫猫

(1+1/2)(1－1/2)(1+1/3)(1－1/3)(1+1/4)(1－1/4)……(1+1/9999)(1－1/9999)……(1－1/n)(1+1/n)

=(2-1)(3-1)(4-1)(5-1)...(n-1)(2+1)(3+1)(4+1)(5+1)...n(n+1)/[(2.3.4.5...n)(2.3.4.5...n)]

=1.2.3.4.....(n-1)3.4.5.6.....n(n+1))/[(2.3.4.5...n)(2.3.4.5...n)]

=(n+1))/(2n)

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