(2+1)(2^2+1)(2^4+1)...(2^2n+1)+1(n是正整数)计算
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(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](/uploads/image/z/2738746-10-6.jpg?t=%EF%BC%882%2B1%EF%BC%89%EF%BC%882%5E2%2B1%EF%BC%89%EF%BC%882%5E4%2B1%EF%BC%89...%EF%BC%882%5E2n%2B1%EF%BC%89%2B1%EF%BC%88n%E6%98%AF%E6%AD%A3%E6%95%B4%E6%95%B0%EF%BC%89%E8%AE%A1%E7%AE%97)
(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
=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
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