I don't get why this is absolutely convergent?

$\displaystyle \sum^{\infty}_{n=1} \frac{sin(4n)}{7^n}$

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- Mar 29th 2009, 07:47 PMmollymcf2009why is this absolutely convergent?
I don't get why this is absolutely convergent?

$\displaystyle \sum^{\infty}_{n=1} \frac{sin(4n)}{7^n}$ - Mar 29th 2009, 07:54 PMKrizalid
$\displaystyle \left| a_{n} \right|=\frac{\left| \sin 4n \right|}{7^{n}}\le \frac{1}{7^{n}},$ that's why.