（2+1）（2^2+1）（2^4+1）...（2^2n+1）+1（n是正整数）计算_其他解答

（2+1）（2^2+1）（2^4+1）...（2^2n+1）+1（n是正整数）计算

人气：367 ℃　时间：2020-05-13 08:27:55

解答

（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