计算(1+2)(1+2²)(1+2^4)(1+2^8)(1+2^16)

计算(1+2)(1+2²)(1+2^4)(1+2^8)(1+2^16)
计算(1+2)(1+2²)(1+2^4)(1+2^8)(1+2^16)

计算(1+2)(1+2²)(1+2^4)(1+2^8)(1+2^16)
(1+2)(1+2²)(1+2^4)(1+2^8)(1+2^16)
= (1-2)(1+2)(1+2²)(1+2^4)(1+2^8)(1+2^16) / (1-2)
= (1-2²)(1+2²)(1+2^4)(1+2^8)(1+2^16) / (-1)
= - (1-2^4)(1+2^4)(1+2^8)(1+2^16)
= - (1-2^8)(1+2^8)(1+2^16)
= - (1-2^16)(1+2^16)
= 2^32 -1
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(1+2)(1+2²)(1+2^4)(1+2^8)(1+2^16)
= (1-2)(1+2)(1+2²)(1+2^4)(1+2^8)(1+2^16) / (1-2)
= (1-2²)(1+2²)(1+2^4)(1+2^8)(1+2^16) / (-1)
= - (1-2^4)(1+2^4)(1+2^8)(1+2^16)
= -...

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(1+2)(1+2²)(1+2^4)(1+2^8)(1+2^16)
= (1-2)(1+2)(1+2²)(1+2^4)(1+2^8)(1+2^16) / (1-2)
= (1-2²)(1+2²)(1+2^4)(1+2^8)(1+2^16) / (-1)
= - (1-2^4)(1+2^4)(1+2^8)(1+2^16)
= - (1-2^8)(1+2^8)(1+2^16)
= - (1-2^16)(1+2^16)
= 2^32 -1
也就是利用平方差公式，先乘以一个（1-2）再除以一个（1-2），使其与原式依旧相等，然后就可以利用平方差公式计算

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