化简:(3+1)(3^2+1)(3^4+1)...(3^2n+1)
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![化简:(3+1)(3^2+1)(3^4+1)...(3^2n+1)](/uploads/image/z/5915242-10-2.jpg?t=%E5%8C%96%E7%AE%80%3A%283%2B1%29%283%5E2%2B1%29%283%5E4%2B1%29...%283%5E2n%2B1%29)
化简:(3+1)(3^2+1)(3^4+1)...(3^2n+1)
化简:(3+1)(3^2+1)(3^4+1)...(3^2n+1)
化简:(3+1)(3^2+1)(3^4+1)...(3^2n+1)
(3+1)(3^2+1)(3^4+1)...(3^2n+1)
=(3-1)(3+1)(3^2+1)(3^4+1)...(3^2n+1)/2
=(3^2-1)(3^2+1)(3^4+1)...(3^2n+1)/2
=(3^2n-1)(3^2n+1)/2
=(3^4n-1)/2
先在原式上乘以(3-1)再除以(3-1) 分子利用平方差公式得 3^16-1 所以最后结果为(3^16-1)/2