(2+1)(2^2+1)(2^4+1)……(2^(2n)+1)的值是( ) A.4^(2n)-1 B.2^2^(2n) C.2^(2n)-1 D.2^n-1
问题描述:
(2+1)(2^2+1)(2^4+1)……(2^(2n)+1)的值是( ) A.4^(2n)-1 B.2^2^(2n) C.2^(2n)-1 D.2^n-1
答
(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)
=...
=(2^(2n)-1)(2^(2n)+1)
=4^(2n)-1
选A