[1+2^(-0.0625)][1+2^(-0.125)][1+2^(-0.25)][1+2^(-0.5)]
来源:学生作业帮助网 编辑:作业帮 时间:2024/11/08 00:52:18
[1+2^(-0.0625)][1+2^(-0.125)][1+2^(-0.25)][1+2^(-0.5)]
[1+2^(-0.0625)][1+2^(-0.125)][1+2^(-0.25)][1+2^(-0.5)]
[1+2^(-0.0625)][1+2^(-0.125)][1+2^(-0.25)][1+2^(-0.5)]
[1+2^(-0.0625)][1+2^(-0.125)][1+2^(-0.25)][1+2^(-0.5)]
=[1+2^(-1/16)][1+2^(-1/8)][1+2^(-1/4)][1+2^(-1/2)]
=[1-2^(-1/16)][1+2^(-1/16)][1+2^(-1/8)][1+2^(-1/4)][1+2^(-1/2)]/[1-2^(-1/16)]
=[(1-2^(-1)]/[1-2^(-1/16)]
=(1/2)/[1-(1/2)^(1/16)]
因为
[1-2^(-0.0625)][1+2^(-0.0625)][1+2^(-0.125)][1+2^(-0.25)][1+2^(-0.5)]
=[1-2^(-0.125)][1+2^(-0.125)][1+2^(-0.25)][1+2^(-0.5)]
=[1-2^(-0.25)][1+2^(-0.25)][1+2^(-0.5)]
=[1-2^(-0.5)][1+...
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因为
[1-2^(-0.0625)][1+2^(-0.0625)][1+2^(-0.125)][1+2^(-0.25)][1+2^(-0.5)]
=[1-2^(-0.125)][1+2^(-0.125)][1+2^(-0.25)][1+2^(-0.5)]
=[1-2^(-0.25)][1+2^(-0.25)][1+2^(-0.5)]
=[1-2^(-0.5)][1+2^(-0.5)]
=1-2^(-1)
=1/2
所以
[1+2^(-0.0625)][1+2^(-0.125)][1+2^(-0.25)][1+2^(-0.5)]
=(1/2)/[1-2^(-0.0625)]
=1/[2-2^(0.9325)]
≈-10.94
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