(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)怎么算啊急用!
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![(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)怎么算啊急用!](/uploads/image/z/59998-22-8.jpg?t=%283%2B1%29%283%5E2%2B1%29%283%5E4%2B1%29%283%5E8%2B1%29%283%5E16%2B1%29%E6%80%8E%E4%B9%88%E7%AE%97%E5%95%8A%E6%80%A5%E7%94%A8%21)
(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)怎么算啊急用!
(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)怎么算啊
急用!
(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)怎么算啊急用!
(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)-1
=1/2*(3-1)*(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)-1
=1/2(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)-1
=1/2*(3^4-1)(3^4+1)(3^8+1)(3^16+1)-1
=1*2(3^8-1)(3^8+1)(3^16+1)-1
=1/2*(3^16-1)(3^16+1)-1
=1/2(3^32-1)-1
=1/2(3^32+1)
=3^32/2+1/2
乘以(3-1)/2变成:
(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)
类推:最后是3^32-1...
(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)/2
=(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)/2
=(3^4-1)(3^4+1)(3^8+1)(3^16+1)/2
=(3^8-1)(3^8+1)(3^16+1)/2
=(3^16-1)(3^16+1)/2
=(3^32-1)/2