why is this absolutely convergent?

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March 29th 2009, 07:47 PM
mollymcf2009

why is this absolutely convergent?

I don't get why this is absolutely convergent?

$\sum^{\infty}_{n=1} \frac{sin(4n)}{7^n}$
March 29th 2009, 07:54 PM
Krizalid

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

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