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利用平方差公式或逆用平方差公式计算!必须正确,有高赏.
(2+1)(4+1﹚﹙16+1﹚﹙256+1)=
(1+1/2)(1+1/4)(1+1/16)(1+1/256)(1/65536)=
(1-1/2)(1-1/9)(1-1/16)…(1-1/100)=
人气:155 ℃ 时间:2020-02-05 21:10:33
解答
(2+1)(4+1﹚﹙16+1﹚﹙256+1)=【(2-1)*(2+1)】*(4+1)*(16+1)*(256+1)
={【4-1】*(4+1)}*(16+1)*(256+1)
=(16-1)*(16+1)*(256+1)
=(256-1)*(256+1)=65536-1=65535
(1+1/2)(1+1/4)(1+1/16)(1+1/256)(1/65536)
={2*(1-1/2)(1+1/2)}(1+1/4)(1+1/16)(1+1/256)(1/65536)=2*{1-1/4}(1+1/4)(1+1/16)(1+1/256)(1/65536)
=2*(1+1/16)(1+1/16)(1+1/256)(1/65536)
=2*(1-1/256)(1+1/256)(1/65536)=2*(1-1/65536)(1+1/65536)=8589934592/4294907296
(1-1/2)(1-1/9)(1-1/16)…(1-1/100)={3/2*(1+1/2)(1-1/2)}{1-(1/3)^2}{1-(1/4)^2}.1-
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