0
$\begingroup$

Possible Duplicate:
What does recursive cosine sequence converge to?

Consider the following sequence defined as follows:

$x_0 =1.$ $x_{n+1} = \cos(x_n)$

How do I show that $x_n$ is convergent?

  • 1
    (One of the answers has a proof of convergence)2012-03-01
  • 0
    You are doing what is sometimes called a fixed point iteration. If you can prove that the derivative (of $\cos x)$ stays below $c$ in absolute value, where $c$ is a definite number less than $1$, then there is convergence. Note that being $<1$ in absolute value is not enough.2012-03-01

0 Answers 0