（2加1）乘（2的平方加1)乘（2的四次方加1）乘...（2的三十二次方加1）加1怎么算呀

Question

（2加1）乘（2的平方加1)乘（2的四次方加1）乘...（2的三十二次方加1）加1怎么算呀

Answer 1

(2+1)(2^2+1)(2^4+1)*.*(2^32+1)+1
=(2-1)(2+1)(2^2+1)(2^4+1)*.*(2^32+1)+1
=(2^2-1)(2^2+1)(2^4+1).(2^32+1)+1
=(2^4-1)(2^4+1).(2^32+1)+1
.
=(2^32-1)(2^32+1)+1
=2^64-1+1
=2^64.