计算(2+1)(2^2+1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)!

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/08 13:12:06
计算(2+1)(2^2+1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)!

计算(2+1)(2^2+1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)!
计算(2+1)(2^2+1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)!

计算(2+1)(2^2+1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)!
(2+1)(2^2+1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)
=(2-1)[(2+1)(2^2+1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)]
=[(2-1)(2+1)](2^2+1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)
=(2^2-1)(2^2+1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)
=[(2^2-1)(2^2+1)](2^4+1)(2^6+1)(2^8+1)……(2^2n+1)
=(2^4-1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)
...
=(2^2n -1)(2^2n+1)
=2^(2n+2)-1