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

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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在数列{an}中a1=a,a(n+1)+2an=2^(n+1)a=8/9

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
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

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
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,公比为-1的等比数列.
因a=8/9不为1,因此,
a(n)/2^n - 1/2 = [(a-1)/2](-1)^(n-1) = (-1/18)(-1)^(n-1).
a(n)/2^n = 1/2 - (1/18)(-1)^(n-1),
a(n) = 2^(n-1) + (1/18)(-2)^n

a(n+1)+2an=2^(n+1)
a(n+1)/2^(n+1) - an/2^n=1
{an/2^n}是等差数列, d=1
an/2^n-a1/2^1=n-1
an/2^n = n- 5/9
an/2^n -1/2= n- 7/4
{an/2^n-1/2不是等比数列