Math Help - why is this absolutely convergent?

1. why is this absolutely convergent?

I don't get why this is absolutely convergent?

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

2. $\left| a_{n} \right|=\frac{\left| \sin 4n \right|}{7^{n}}\le \frac{1}{7^{n}},$ that's why.