# Math Help - Series Expansion

1. ## Series Expansion

What is the coefficient of in the power series expansion of ?

I'm having trouble expanding this. Could someone explain how to solve it? Cheers.

2. Originally Posted by Haris
What is the coefficient of in the power series expansion of ?

I'm having trouble expanding this. Could someone explain how to solve it? Cheers.
you don't need to expand anything

let $f(x) = \frac 1{(9 + 5x)^{1/4}}$

the coefficient of the $x^2$-term is given by

$\frac {f''(0)}{2!}$

3. Originally Posted by Haris
What is the coefficient of in the power series expansion of ?

I'm having trouble expanding this. Could someone explain how to solve it?
Write it as $9^{-1/4}\bigl(1+\tfrac{5x}9\bigr)^{-1/4}$. Then use the binomial expansion of $(1+t)^{-1/4}$, taking t=5x/9.

Edit. Alternatively, use Jhevon's method. It's equally good.