# Series Expansion

• January 26th 2009, 08:53 AM
Haris
Series Expansion
What is the coefficient of http://ta2.maths.ed.ac.uk:8080/maple...fdmnpjlelp.gif in the power series expansion of http://ta2.maths.ed.ac.uk:8080/maple...ccgpmmnkoh.gif?

I'm having trouble expanding this. Could someone explain how to solve it? Cheers.
• January 26th 2009, 10:06 AM
Jhevon
Quote:

Originally Posted by Haris
What is the coefficient of http://ta2.maths.ed.ac.uk:8080/maple...fdmnpjlelp.gif in the power series expansion of http://ta2.maths.ed.ac.uk:8080/maple...ccgpmmnkoh.gif?

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

$\frac {f''(0)}{2!}$
• January 26th 2009, 10:08 AM
Opalg
Quote:

Originally Posted by Haris
What is the coefficient of http://ta2.maths.ed.ac.uk:8080/maple...fdmnpjlelp.gif in the power series expansion of http://ta2.maths.ed.ac.uk:8080/maple...ccgpmmnkoh.gif?

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.