# Converging series problem

• June 9th 2013, 07:16 AM
jgv115
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!
• June 9th 2013, 07:22 AM
alteraus
Re: Converging series problem
hi, I would use that $a_n \leq 3 \,,\,\forall n$ so
$\sum_{n=0}^{\infty}\frac{a_n}{4^n}\leq\sum_{n=0}^{ \infty}\frac{3}{4^n}=3\sum_{n=0}^{\infty}\frac{1}{ 4^n}$
• June 9th 2013, 07:25 AM
jgv115
Re: Converging series problem
Wow! You're a genius. So simple!!!

Thanks a lot alteraus