试求(2+1)(2²+1)(2的四次方+1）...（2的2n次方+1）+1的值.

试求(2+1)(2²+1)(2的四次方+1）...（2的2n次方+1）+1的值.
试求(2+1)(2²+1)(2的四次方+1）...（2的2n次方+1）+1的值.

试求(2+1)(2²+1)(2的四次方+1）...（2的2n次方+1）+1的值.
(2+1)(2^2+1)(2^4+1)(2^8+1)...(2^2n+1)
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)...(2^2n+1) 　　　原式乘以1,即乘以(2-1),值不变
=(2^2-1)(2^2+1)(2^4+1)...(2^2n+1) 往下递次使用平方差公式(a-1)(a+1)=a^2-1
=(2^4-1)(2^4+1)(2^8+1)...(2^2n+1)
=(2^8-1)(2^8+1)...(2^2n+1)
=(2^2n-1)(2^2n+1)
=2^4n-1