The function f(x)=9/(1+49x^2) is represented as a power series

Find the first few coefficients in the power series.

I got the first few coefficients, but can't figure out the radius of convergence. Can someone help?

Question

The function f(x)=9/(1+49x^2) is represented as a power series 

Find the first few coefficients in the power series. 

I got the first  few coefficients, but can't figure out the radius of convergence.  Can someone help?

anonymous · Answer

$$f(x)=\frac{ 9 }{ (1+49^{2}) }$$

gives 

$$9(1-(49x^2)+(49x^2)^2$$

so 

c0=  9
c1=  0
c2=  -441
c3=  0
c4=  21609

but how do i find the radius of convergence?

anonymous · Answer

@saiken2009

anonymous · Answer

i know my C's are right.  i need the radius of convergence. thanks

anonymous · Answer

can someone please help?  i didn't need help finding the C's.  i already found them.  the ones @UditKulka wrote are wrong anyway.  

please help

terenzreignz · Answer

@saiken2009 Hi ^_^
I don't know how to get the radius of convergence (normally) but when faced with a function of this form
$$\Large \frac{a}{1\pm u}$$
This is represented by the power series
$$\Large a\sum_{n=0}^\infty(\mp u)^n$$ 
BUT ONLY
if $\large |u|<1$
Now, it just so happens that in this case, your $\large u = 49x^2$
can you work it out from here?