[obm-l] Seq��ncia recursiva

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Subject: [obm-l] Seq��ncia recursiva
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Date: Mon, 15 Oct 2007 00:41:03 -0300
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Achei esse problema em um livro de An�lise e estou tendo dificuldades em resolv�-lo. � poss�vel achar o termo geral em fun��o de a_1 e n?

Seja (x_n) uma seq��ncia definida indutivamente por x_1 > 3 e x_{n+1} = 4 – 3/x_n, n natural. Mostre que

a) x_n > 3, para cada n natural.

b) (x_n) � decrescente.

c) (x_n) converge e que seu limite � 3.

Agrade�o a ajuda.

Henrique.

Follow-Ups:
- Re: [obm-l] Seq��ncia recursiva
  - From: Nicolau C. Saldanha