# Math Help - Power Series Representation Question Help

1. ## Power Series Representation Question Help

Hi can someone please help me with the foloowing question. Thanks.

Find a power series representation for the following functions:
(a) f(x) =

x^
3/(3 + x^2)^2 :
(b)

f(x) = x^2 ln( cuberoot(2 + x^3)):
(c)

f(x) = 1/x about x0 = 3.

Thank you to all who help in advance.

2. Originally Posted by engineeringboy
Hi can someone please help me with the foloowing question. Thanks.

Find a power series representation for the following functions:
(a) f(x) =

x^
3/(3 + x^2)^2 :

$f(x)=\frac{x^3}{(3+x^2)^2}=\frac{x^3}{9} \times \frac{1}{(1+x^2/3)^2}$

Now expand the second part of the right hand side using the binomial expansion of $1/(1+u)^2$ with $u=x^2/3$ then simplify.

CB