(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)具体怎么做
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![(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)具体怎么做](/uploads/image/z/379357-61-7.jpg?t=%283%2B1%29%283%5E2%2B1%29%283%5E4%2B1%29%283%5E8%2B1%29%283%5E16%2B1%29%E5%85%B7%E4%BD%93%E6%80%8E%E4%B9%88%E5%81%9A)
(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)具体怎么做
(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)具体怎么做
(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)具体怎么做
(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)
=(1/2)(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)
=(1/2)(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)
=(1/2)(3^4-1)(3^4+1)(3^8+1)(3^16+1)
=(1/2)(3^8-1)(3^8+1)(3^16+1)
=(1/2)(3^16-1)(3^16+1)
=(1/2)(3^32-1)
=3^32/2-1/2
(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)
=(3-1)*(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)/(3-1)
=(3^32-1)/2
=3^32/2-1/2
这个是连用平方差公式:只要你给前面加一个(3-1)再给他们×二分之一就可以了
就那么做啊
整个式子乘以一个(3-1)再除以一个(3-1),结果等于(3^16-1)(3^16+1)/(3-1)=(3^32-1)/2