Consider the following function.

$f(x)=\frac{5}{9+2x}$

a$.$ Find the full power series of $f(x)$ centered at $x=0$ and give the first five nonzero terms.

$f(x)={\displaystyle \underset{n=0}{\overset{}{}}}$

$=++++$cdots$+$

$$

$+$

b$.$ Compute the open interval of convergence corresponding to the power series found in Part a$.$ Give your answer in interval notation.

Open interval of convergence: $$