在数列{an}中a1=a,a（n+1）+2an=2^(n+1）a=8/9,试问数列{an/2^n-1/2}能否为等比数列求详细谢

Question

在数列{an}中a1=a,a（n+1）+2an=2^(n+1）
a=8/9,试问数列{an/2^n-1/2}能否为等比数列求详细谢

Answer 1

a(n+1) = -2a(n) + 2^(n+1),a(n+1)/2^(n+1) = -a(n)/2^n + 1 = -a(n)/2^n + 1/2 + 1/2,a(n+1)/2^(n+1) - 1/2 = -a(n)/2^n + 1/2 = -[a(n)/2^n - 1/2]{a(n)/2^n - 1/2}是首项为a(1)/2 - 1/2 = a/2 - 1/2 = (a-1)/2,公...