(1-1/4×(1-1/9)×(1-1/16)×...×(1-1/10000)怎么解急

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(1-1/4×(1-1/9)×(1-1/16)×...×(1-1/10000)怎么解急

(1-1/4×(1-1/9)×(1-1/16)×...×(1-1/10000)怎么解急
(1-1/4×(1-1/9)×(1-1/16)×...×(1-1/10000)怎么解

(1-1/4×(1-1/9)×(1-1/16)×...×(1-1/10000)怎么解急
(1-1/4)×(1-1/9)×(1-1/16)×...×(1-1/10000)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)……(1-1/100)(1+1/100)
=(1/2)(3/2)(2/3)(4/3)(3/4)(5/4)……(99/100)(101/100)
=(1/2)*(101/100)
=101/200
中间项两两抵消了.

用平方差公式打开,然后约分,答案:101/200