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(1+1/2)(1+1/2的平方)(1+1/2的四次方)(1+1/2的八次方)(1+1/2的十六次方)+(1+2的31次方)
人气:285 ℃ 时间:2020-04-06 10:47:28
解答
(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)+(1+2^31)=(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)/(1-1/2)+ 1+1/2^31
=(1-1/2²)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)/(1-1/2)+ 1+1/2^31
=(1-1/2^4)(1+1/2^4)(1+1/2^8)(1+1/2^16)/(1-1/2)+ 1+1/2^31
=(1-1/2^8)(1+1/2^8)(1+1/2^16)/(1-1/2)+ 1+1/2^31
=(1-1/2^16)(1+1/2^16)×2+ 1+1/2^31
=2-1/2^31+1+1/2^31
=3
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