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Re: Limit of sequence
*To*: mathgroup at smc.vnet.net
*Subject*: [mg25298] Re: [mg25276] Limit of sequence
*From*: BobHanlon at aol.com
*Date*: Tue, 19 Sep 2000 03:45:20 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
In a message dated 9/17/2000 5:54:09 PM, none at none.com writes:
>Can Mathematica find the limit of a sequence?
>As I understood, it treats the argument of the Limit function as a real
>variable,
>therefore the limit of Sin[Pi*n] turns out to be undefined.
>
Simplify[Sin[Pi*n], Element[n, Integers]]
0
As an example of finding the limit of a sequence:
Needs["DiscreteMath`RSolve`"]
Let
eqn = {a[n] == a[n - 1] + a[n - 2], a[0] == a[1] == 1};
and the sequence for which the limit is desired be a[n]/a[n-1]
soln = (a[n] /. (RSolve[eqn, a[n], n] // Flatten))
(2^(-1 - n)*(-(1 - Sqrt[5])^(1 + n) +
(1 + Sqrt[5])^(1 + n)))/Sqrt[5]
ratio = soln/(soln /. n -> (n - 1));
lim = Limit[ratio, n -> Infinity]
1/2*(1 + Sqrt[5])
FullSimplify[lim - GoldenRatio] == 0
True
Bob Hanlon
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