Math Help - Converging series problem

1. Converging series problem

How would I go about proving that this series converges:

$\sum^{\infty}_{n=0} \frac{a_n}{4^n}$

Where $a_n$ is the sequence $1,2,3,1,2,3,...$

Any pointers would be kindly appreciated!

2. Re: Converging series problem

hi, I would use that $a_n \leq 3 \,,\,\forall n$ so
$\sum_{n=0}^{\infty}\frac{a_n}{4^n}\leq\sum_{n=0}^{ \infty}\frac{3}{4^n}=3\sum_{n=0}^{\infty}\frac{1}{ 4^n}$

3. Re: Converging series problem

Wow! You're a genius. So simple!!!

Thanks a lot alteraus