Hello!!! According to my lecture notes, the radius of convergence of the power series $p(x)= \sum_{n=0}^{\infty} (-2) x^{2n+1}, -1<x<1$ and $q(x)= \sum_{n=0}^{\infty} p(p+1) x^{2n}, -1<x<1$ is 1.
Could you explain me why they are equal to 1.
It holds that $R= \frac{1}{\limsup_{n \to +\infty} \sqrt[n]{|a_n|}}$.
Are the following , $\frac{1}{\limsup_{n \to +\infty} \sqrt[n]{2}}$, $\frac{1}{\limsup_{n \to +\infty} \sqrt[n]{p(p+1)}}$ equal to 1?