Hiya guys!

I'd really appreciate some help with this question, I don't even know where to begin!This book I'm using is rubbish!

Consider the sequence $\displaystyle (a_{n})$, where

$\displaystyle a_{1}=0$, $\displaystyle a_{n+1}=\frac{3a_{n}+1}{a_{n}+3}$ $\displaystyle (n\geq1)$

a.) Show by induction that $\displaystyle 0\leq{a_{n}}<1$

b.) Show that $\displaystyle a_{n}$ is monotonic increasing

But where do I go about getting $\displaystyle a_{n}$ in the first place?? I'd really appreciate a full explaination. Thanks so much guys!

Jo