(2+1)(2^2+1)(2^4+1)……(2^2n+1)
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![(2+1)(2^2+1)(2^4+1)……(2^2n+1)](/uploads/image/z/11602883-11-3.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%E2%80%A6%E2%80%A6%EF%BC%882%5E2n%2B1%EF%BC%89)
(2+1)(2^2+1)(2^4+1)……(2^2n+1)
(2+1)(2^2+1)(2^4+1)……(2^2n+1)
(2+1)(2^2+1)(2^4+1)……(2^2n+1)
(2+1)(2^2+1)(2^4+1)……(2^2n+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)
=(2^4-1)*(2^4+1)……(2^2n+1)
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=(2^2n-1)(2^2n+1)
=2^4n-1
(2+1)(2^2+1)(2^4+1)……(2^2n+1)=2^4n-1