作业帮求(3+1)(3²+1)(3^4+1)···(3^2n+1)的值
来源：学生作业帮助网 编辑：作业帮 时间：2024/06/12 06:55:46
求(3+1)(3²+1)(3^4+1)···(3^2n+1)的值
(3+1)(3²+1)(3^4+1)···(3^2n+1)
=（3-1)(3+1)(3²+1)(3^4+1)···(3^2n+1)/(3-1)
=(3²-1)(3²+1)(3^4+1)···(3^2n+1)/2
=(3^4-1)(3^4+1)···(3^2n+1)/2
=(3^8-1)···(3^2n+1)/2
………………………………
=(3^4n-1)/2
(3+1)(3²+1)(3^4+1)···(3^2n+1)
=(3-1)(3+1)(3²+1)(3^4+1)···(3^2n+1)/(3-1)
=(3^4n-1)/2