来自钱素琴的问题
(2+1)(2^2+1)(2^4+1)...(2^2n+1)+1(n是正整数)计算
(2+1)(2^2+1)(2^4+1)...(2^2n+1)+1(n是正整数)计算
1回答
2020-06-20 17:59
(2+1)(2^2+1)(2^4+1)...(2^2n+1)+1(n是正整数)计算
(2+1)(2^2+1)(2^4+1)...(2^2n+1)+1(n是正整数)计算
(2+1)(2^2+1)(2^4+1)...(2^2n+1)+1
=1*(2+1)(2^2+1)(2^4+1)...(2^2n+1)+1
=(2-1)(2+1)(2^2+1)(2^4+1).(2^2n+)+1
=(2^2-1)(2^2+1)(2^4+1).(2^2n+1)+1
=(2^4-1)(2^4+1).(2^2n+1)+1
=(2^8-1).(2^2n+1)+1
=(2^2n-1)(2^2n+1)+1
=2^4n-1+1
=2^4n