(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^16

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(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^16
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(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^16
(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^16

(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^16
原式=(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)/(1-1/2)+1/2^16
=2(1-1/2^16)+1/2^16 前面每两项结合为平方差公式
=2-1/2^16