计算:(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/07 11:50:19
计算:(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)
![计算:(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)](/uploads/image/z/8650423-55-3.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%9A%283%2B1%29%283%5E2%2B1%29%283%5E4%2B1%29%283%5E8%2B1%29%283%5E16%2B1%29)
(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
=(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