Question

这是一道利用平方差公式计算的题目，求帮忙。

Answer 1

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