How would I go about proving that this series converges:

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

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

Any pointers would be kindly appreciated!

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- Jun 9th 2013, 07:16 AMjgv115Converging series problem
How would I go about proving that this series converges:

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

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

Any pointers would be kindly appreciated! - Jun 9th 2013, 07:22 AMalterausRe: Converging series problem
hi, I would use that $\displaystyle a_n \leq 3 \,,\,\forall n$ so

$\displaystyle \sum_{n=0}^{\infty}\frac{a_n}{4^n}\leq\sum_{n=0}^{ \infty}\frac{3}{4^n}=3\sum_{n=0}^{\infty}\frac{1}{ 4^n}$ - Jun 9th 2013, 07:25 AMjgv115Re: Converging series problem
Wow! You're a genius. So simple!!!

Thanks a lot alteraus