# Math Help - Interval of Convergence

1. ## Interval of Convergence

So, I've been trying to figure out this problem for an hour now, and I keep on getting the same answer which isn't correct and I'm not exactly sure what I'm doing wrong.
The question is attached.

It asks for the left and right end of convergence.
So I applied the ratio test, and I keep on getting:
x<3 x>15

When I take the limit in the ratio test, I'm left with (x+6)/9. So I set it for when the abs value of x is less than one... and I get the answers above.

If anyone could help that would be great!!

2. Algebra, algebra, where is the algebra?
$\begin{array}{l}
- 1 < \frac{{x + 6}}{9} < 1 \\
- 9 < x + 6 < 9 \\
- 15 < x < 3 \\
\end{array}
$