计算:2(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)+1
来源:学生作业帮 编辑:搜搜考试网作业帮 分类:数学作业 时间:2024/07/02 01:54:04
计算:2(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)+1
![计算:2(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)+1](/uploads/image/z/6418184-32-4.jpg?t=%E8%AE%A1%E7%AE%97%3A2%283%2B1%29%283%5E2%2B1%29%283%5E4%2B1%29%283%5E8%2B1%29%283%5E16%2B1%29%2B1)
2(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)+1
=(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)+1
=(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)+1
=(3^4-1)(3^4+1)(3^8+1)(3^16+1)+1
=(3^8-1)(3^8+1)(3^16+1)+1
=(3^16-1)(3^16+1)+1
=3^32-1+1
=3^32
=(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)+1
=(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)+1
=(3^4-1)(3^4+1)(3^8+1)(3^16+1)+1
=(3^8-1)(3^8+1)(3^16+1)+1
=(3^16-1)(3^16+1)+1
=3^32-1+1
=3^32