(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)，最后一步“=(2^32-1）/2^31”是怎么得出来，请详细解答
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解决时间 2021-04-07 12:27
- 提问者网友：风月客
- 2021-04-06 19:09
(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)，最后一步“=(2^32-1）/2^31”是怎么得出来，请详细解答
最佳答案
- 五星知识达人网友：天凉才是好个秋
- 2020-11-02 07:52
先乘以(1-1/2) ,再除以(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)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)÷(1-1/2)
=(1-1/2²)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)×2
=(1-1/2^4)(1+1/2^4)(1+1/2^8)(1+1/2^16)×2
=(1-1/2^8)(1+1/2^8)(1+1/2^16)×2
=(1-1/2^16)(1+1/2^16)×2
=(1-1/2^32)×2
=[(2^32-1)/2^32]×2
=(2^32-1）/2^31
(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)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)÷(1-1/2)
=(1-1/2²)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)×2
=(1-1/2^4)(1+1/2^4)(1+1/2^8)(1+1/2^16)×2
=(1-1/2^8)(1+1/2^8)(1+1/2^16)×2
=(1-1/2^16)(1+1/2^16)×2
=(1-1/2^32)×2
=[(2^32-1)/2^32]×2
=(2^32-1）/2^31
全部回答
- 1楼网友：山河有幸埋战骨
- 2020-04-19 02:15
(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)+1/2^31
=2*(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)+1/2^31
=2(1-1/2^2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)+1/2^31
=2(1-1/2^4)(1+1/2^4)(1+1/2^8)(1+1/2^16)+1/2^31
=2(1-1/2^32)+1/2^31
=2
=
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