(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)计算

发布网友 发布时间:2024-12-18 05:20

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热心网友 时间:2025-01-09 18:23

设原式结果为A 即(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)=A
考虑:
1/2A= (1-1/2)A
=(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)
=(1-1/2^2)(1+1/2^2)(1+1/2^4)(1+1/2^8)
=(1-1/2^4)(1+1/2^4)(1+1/2^8)
=(1-1/2^8)(1+1/2^8)
= 1- 1/2^16

所以A=2(1- 1/2^16) = 2 - 1/2^15

热心网友 时间:2025-01-09 18:24

用平方差公式,分子分母同乘(1-1/2)
(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)
=(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)/(1-1/2)
=(1-1/2^2)(1+1/2^2)(1+1/2^4)(1+1/2^8)/(1-1/2)
=(1-1/2^4)(1+1/2^4)(1+1/2^8)/(1-1/2)
=(1-1/2^8)(1+1/2^8)/(1-1/2)
=(1-1/2^16)/(1-1/2)
=2*(1-1/2^16)

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