数列{an},a1=1,a(n+1)=2an-n^2+3n

题目

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

答案

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...