- #1

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## Homework Statement

Given:

[tex]x_{n+1}=\frac{1}{3+x_n}[/tex]

with

[tex] x_1=1 [/tex]

Show that:

(1)

[tex]|x_{n+1}-x_n| \leq \frac{1}{9}|x_{n}-x_{n-1}|[/tex]

and (2) x_n is Cauchy.

## Homework Equations

## The Attempt at a Solution

I've tried different approaches (including induction) but the sequence isn't monotonically decreasing.