(1+1/2)(1+1/4)(1+1/16)(1+1/256)+1/32768等于多少第四个是八

(1+1/2)(1+1/4)(1+1/16)(1+1/256)+1/32768等于多少第四个是八
(1+1/2)(1+1/4)(1+1/16)(1+1/256)+1/32768等于多少

第四个是八

(1+1/2)(1+1/4)(1+1/16)(1+1/256)+1/32768等于多少第四个是八
=(1-1/2)(1+1/2)(1+1/4)(1+1/16)(1+1/256)*2 + 1/2^15
=(1-1/2^16)*2+ 1/2^15
=2-2/(2^16)+ 1/2^15
=2

=(1-1/2)(1+1/2)(1+1/2²)(1+1/2的4次方)(1+1/2的8次方)÷(1-1/2)+1/2的15次方
=(1-1/2²)(1+1/2²)(1+1/2的4次方)(1+1/2的8次方)÷(1-1/2)+1/2的15次方 前面二个相乘
=(1-1/2的4次方)(1+1/2的4次方)(1+1/2的8次方)÷(1...

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=(1-1/2)(1+1/2)(1+1/2²)(1+1/2的4次方)(1+1/2的8次方)÷(1-1/2)+1/2的15次方
=(1-1/2²)(1+1/2²)(1+1/2的4次方)(1+1/2的8次方)÷(1-1/2)+1/2的15次方 前面二个相乘
=(1-1/2的4次方)(1+1/2的4次方)(1+1/2的8次方)÷(1-1/2)+1/2的15次方
=(1-1/2的8次方)(1+1/2的8次方)÷(1-1/2)+1/2的15次方
=(1-1/2的16次方)÷1/2+1/2的15次方
=2-1/2的15次方 +1/2的15次方
=2

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先计算
(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)
设a=(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)
那么
(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)
=...

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先计算
(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)
设a=(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)
那么
(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
因此
a=2-1/2^8
原式
=a+1/2^8
=2

收起

3／25／417／16257／256=32767／32768

你好幽默啊！拿人消遣是吧

∵原式/2=(1/2)(1+1/2)(1+1/4)(1+1/16)(1+1/256) +1/2^16
=(1-1/2)(1+1/2)(1+1/4)(1+1/16)(1+1/256) +1/2^16
=(1-1/4)(1+1/4)(1+1/16)(1+1/256) +1/2^16
=(1-1/16)(1+1/16)(1+1/256)+1/2^16
=(1-1/256)(1+1/256) +1/2^16
=1-1/2^16 +1/2^16
=1
∴原式=1*2=2