I need to find a Maclaurin series for f(x) = 3x^2 / (4+5x^3) and the radius of convergence

Question

anonymous · Answer

Is this the kind where its f(x)= $$f(0)+f'(0)+f"(0) +... f^n(0)+...$$

anonymous · Answer

yes it is...

anonymous · Answer

I'm sorry, my brain is not working properly.... I was about to just take the integral and substitute but I realize that there is an easier way (I just can't remember). Sorry :/

anonymous · Answer

I'm just not sure if I should start out by trying to put it into the form of 1/(1-x) first?  I'm having trouble with that tho...so I thought that perhaps I'd try putting it into binomial form of (1+x)^k...

anonymous · Answer

Don't quote me on it, but i think its $$3/4 \sum_{n=0}^{\infty}(5/4)^nx^{3n+2}$$ It would be nice if you got the final answer to compare... I'm not sure about it though

anonymous · Answer

ouchie, there should be (-1)^n in it