在数列an中,a1=1,a（n+1）=2an+2^n设bn=an/2^(n-1),bn为等差数列

Question

在数列an中,a1=1,a（n+1）=2an+2^n
设bn=an/2^(n-1),bn为等差数列

Answer 1

证明：b(n+1)-bn=a(n+1)/2^n-an/2^(n-1)
=(2an+2^n)/2^n-an/2^(n-1)
=(2an+2^n)/2^n-2an/2^n
=2^n/2^n
=1
所以bn是等差数列