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Does $f(n+1)/f(n)$ converge as $n\rightarrow\infty$ for $f(n)$ defined by a linear recursion, for all linear recursions?

  • 0
    You're not putting any restrictions on the number of terms?2010-12-27
  • 0
    No, but I think I may have figured it out. All linear recursions can be expressed as an explicit formula right? Then we can just take the limit using the explicit formula and that will always yield a convergence?2010-12-27
  • 1
    I guess you mean linear recursions with constant coefficients? Otherwise there are trivial counterexamples like $f(n+1)=(-1)^n n f(n)$.2010-12-27
  • 5
    I think a precise definition of what you mean by "linear recursion" would be helpful.2010-12-27

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