
计算:(1-2^-2)*(1-3^-2)*...*(1-10^-2)
2个回答
展开全部
原式=(1-1\2)(1+1/2)(1-1/3)(1+1\3)(1-1/4)(1+1/4)……(1-1/9)(1+1/9)(1-1/10)(1+1/10)
=(1/2)(3/2)(2/3)(4/3)(3/4)(5/4)(4/5)……(8/9)(10/9)(9/10)(11/10)
=(1/2)(11/10)
=11/20
=(1/2)(3/2)(2/3)(4/3)(3/4)(5/4)(4/5)……(8/9)(10/9)(9/10)(11/10)
=(1/2)(11/10)
=11/20
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