Given the recursion $f(n) = 2f(n-1) + 2f(n-2) + 2f(n-3)$ starting with $f(0)=f(1)=f(2)=1$, work out the first 10 terms of series. what is the limiting ratio of terms?
I got the series:
But I don't know what is the limiting ratio of terms?
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Dhanvi Sreenivasan
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user3015986
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Your computations are good. The answer is known to be the (unique) real root of equation $x^3=2(x^2+x+1)$ which is the "characteristic equation" of the linear recurrence you give ($x \approx 2.91966$) but its exact expression is awful ! Have you had a lecture on this subject prior to this exercise ? See for example here – Jean Marie Dec 08 '16 at 17:36
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@JeanMarie Thanks for the response but I never had this class. I'm helping my sister with her high school summer camp problem. I don't think she recognizes any of this either. It was suppose to be like a "test" but not graded. I still don't know what the answer is for the limiting ratio of terms. – user3015986 Dec 08 '16 at 17:53