1. Feb 15, 2012

cragar

1. The problem statement, all variables and given/known data
Prove that the sequence defined by $x_1=3$
and $x_{n+1}= \frac{1}{4-x_n}$

3. The attempt at a solution
Well I found like the first 4 terms of this sequence and it seems to be decreasing, heading closer to 0. So this sequence is probably bounded and if it decreasing then it will converge.
If I solve for $x_n$ I get that
$x_n=4- \frac{1}{x_{n+1}}$
So now we see from this that the biggest $x_n$ could be is 4, because it seems that all our numbers are positive. I might need to use that fact that its bounded and decreasing to show that it converges.