Hello! I'm stuck on these questions... Can someone help?
First: how would you write f(x) = x / (1 + x^{3}) as a series?
I mean like
∞
Σ = .....
k=0
I know that 1/(1-x) =
∞
Σ x^{k}
k=0
But how do i convert this into f(x)?
Second: how would you find the radius of convergence of the following binomial series:
∞
Σ (3k k) x^{2k+1}
k=0
with (3k k) is like (n k) = n! / k!(n-k)!
I know how to do it when there's x^{k }in the sommation but with x^{2k+1}?
Thanks for the help, I've been spending hours on these two questions!