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How to find limit of a recursive sequence?

asked 2012-11-24 23:57:16 +0200

anonymous user


For example, I have this sequence: f(0) = 1 f(n) = 1/5 * (f(n-1)^2 + f(n-1) + 3) How do I find the limit of this sequence? I have been searching for how to do this for a while, but I can't find the answer.

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answered 2012-11-25 01:01:40 +0200

achrzesz gravatar image

updated 2012-11-25 04:12:45 +0200

In your example all f(n) are equal to 1, so the limit is 1 :)

In the case of linear recursive definitions you can use rsolve from sympy or solve_rec from Maxima, and then use limit function. In the general nonlinear case you can experiment numerically:

Using Maxima you can do:

sage: maxima('f[n]:=1/5*(f[n-1]^2+f[n-1]+3)')
sage: maxima('f[0]:1')                       
sage: maxima('f[100]')                       
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Asked: 2012-11-24 23:57:16 +0200

Seen: 1,808 times

Last updated: Nov 25 '12