计算 (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16次方)(1+1/2的31次方)

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计算 (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16次方)(1+1/2的31次方)

计算 (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16次方)(1+1/2的31次方)
计算 (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16次方)(1+1/2的31次方)

计算 (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16次方)(1+1/2的31次方)
添加一项(1-1/2)
原式=(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)(1+1/2^32)(1-1/2)/(1-1/2)
=(1-1/2^64)/(1-1/2)=2*(1-1/2^64)
利用平方差公式.
1/2^64 就是2的64次方分之一,也是(1/2)的64次方.

(1+1/2)的62次方

(1+1/2)(1+2/2^2)(1+1/2^4)(1+1/2^8)+1/2^15
=2(1-1/2)(1+1/2)(1+2/2^2)(1+1/2^4)(1+1/2^8)+1/2^15
=2(1-1/2^2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15
=2(1-1/2^4)(1+1/2^4)(1+1/2^8)+1/2^15
=2(1-1/2^8)(1+1/2^8)+1/2^15
=2(1-1/2^16)+1/2^15
=2-1/2^15+1/2^15
=2