# Find power series representation and interval of convergence.

• Nov 21st 2011, 03:41 PM
Intrusion
Find power series representation and interval of convergence.
The problem:

$$f(x) = 1 / (1+9x^2)$$

My attempt:

$f(x) = 1 / (1-(-9x^2)) = \sum (-9x^2)^n = \sum (-1)^n(9x^2)^n$

With |-9x^2| < 1, 9x < 1, x < 1/9
R = 1/9, I = (-1/9, 1/9)

Not sure if this is correct. Thanks
• Nov 21st 2011, 04:15 PM
HallsofIvy
Re: Find power series representation and interval of convergence.
That's a good way to start: you recognized that $\frac{1}{1- r}$ is the sum of the geometric series $\sum r^n$ and here r= -9x^2[/tex]. However, $9x^2< 1$ does NOT give 9x< 1, it gives $9x^2< 1$ so that $-\frac{1}{3}< x< \frac{1}{3}$
• Nov 21st 2011, 09:13 PM
Intrusion
Re: Find power series representation and interval of convergence.
You're right, rookie mistake :D