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MathGroup Archive 2000

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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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