Infinite sequence (recursive)

Let $\displaystyle x_0$ and $\displaystyle k$ be positive real numbers.

$\displaystyle

x_n = \frac{k}{1+x_{n-1}} , \text{ for } n\geq1

$

Now prove that either of the sequences $\displaystyle x_1 , x_3, x_5 \dotsb$ or $\displaystyle x_2 , x_4 , x_6 , \dotsb$ is increasing and the other one is decreasing.

Then prove that $\displaystyle x_1 , x_2 , \dotsb x_n$ is convergant.

I have no idea how to work with recursive sequences, so if someone could tell me how do I start?