数列{an}中,已知a1=5/6,an+1=1/3an+(1/2)^n+1,(n∈N*),
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数列{an}中,已知a1=5/6,an+1=1/3an+(1/2)^n+1,(n∈N*),
且数列a2-1/2a1,a3-1/2a2.an-1/2an-1..是公比为1/3的等比数列,求数列{an}的通项公式.
且数列a2-1/2a1,a3-1/2a2.an-1/2an-1..是公比为1/3的等比数列,求数列{an}的通项公式.
![数列{an}中,已知a1=5/6,an+1=1/3an+(1/2)^n+1,(n∈N*),](/uploads/image/z/6998702-14-2.jpg?t=%E6%95%B0%E5%88%97%7Ban%7D%E4%B8%AD%2C%E5%B7%B2%E7%9F%A5a1%3D5%2F6%2Can%2B1%3D1%2F3an%2B%281%2F2%29%5En%2B1%2C%28n%E2%88%88N%2A%29%2C)
a(n+1)=(1/3)an+(1/2)^(n+1)
a(n+1)-3(1/2)^(n+1) = (1/3)[an - 3(1/2)^n ]
{an - 3(1/2)^n} 是等比数列,q= 1/3
an - 3(1/2)^n = (1/3)^(n-1) .{a1 - 3(1/2)^1}
= -2(1/3)^n
an =3(1/2)^n - 2(1/3)^n
a(n+1)-3(1/2)^(n+1) = (1/3)[an - 3(1/2)^n ]
{an - 3(1/2)^n} 是等比数列,q= 1/3
an - 3(1/2)^n = (1/3)^(n-1) .{a1 - 3(1/2)^1}
= -2(1/3)^n
an =3(1/2)^n - 2(1/3)^n
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