数列{an},a1=1,a(n+1)=2an-n^2+3n
1)是否存在常数λ,μ,使得数列{an+λn^2+μn}是等比数列,若存在,求出λ,μ的值,若不存在说明理由
人气:276 ℃ 时间:2020-03-17 02:36:24
解答
a(n+1)=2an-n^2+3n=2an+(n+1)^2-(n+1)-2n^2+2n将(n+1)^2-(n+1)移过去得a(n+1)-(n+1)^2+(n+1)=2(an-n^2+n)再两边同除(an-n^2+n)得a(n+1)-(n+1)^2+(n+1)/(an-n^2+n)=2所以当λ=-1,μ=1数列{an+λn^2+μn}是等比...
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