# Does the series converge?

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• November 4th 2008, 10:26 AM
veronicak5678
Does the series converge?
Summation from n=1 ti infinity of (sin(1))^n.

How can I break this up? I think it will be a geometric series...
• November 4th 2008, 10:34 AM
Plato
$\left| r \right| < 1 \Rightarrow \quad \sum\limits_{n = 1}^\infty {r^n } = \frac{r}{{1 - r}}$
• November 4th 2008, 10:36 AM
veronicak5678
I thought it was r ^ (n-1)? And what is my r and my a?
• November 4th 2008, 01:12 PM
Mathstud28
Quote:

Originally Posted by veronicak5678
Summation from n=1 ti infinity of (sin(1))^n.

How can I break this up? I think it will be a geometric series...

$|\sin(1)|=|r|<1\Rightarrow\sum)_{n=1}^{\infty}\sin ^n(1)=\frac{\sin(1)}{1-\sin(1)}$
• November 4th 2008, 01:22 PM
veronicak5678
Got it. Thank you!