How can I determine the convergence radius of the following power series:
$F(n,z):=\sum_{j=0}^nz^{3j^2}+5z^{j^3}$ ?
I've tried with the formulas
$ r=\frac{1}{\limsup_{n \to \infty} \sqrt{|a_n|}} $ and $r = \lim_{n \to \infty} |\frac{a_n}{a_{n+1}}|$ but hadn't any success yet.
Best Answer
Assuming that you mean the series $\sum_{j=0}^\infty z^{3j^2}+5z^{j^3}$, then:
So, the radius of convergence is equal to $1$.