Hi all,

Find an example of two power series $\displaystyle \sum a_{n}x^{n}$ and $\displaystyle \sum b_{n}x^{n}$ that have radii of convergence and respectively, such that the cauchy product $\displaystyle \sum c_{n}x^{n}$ ( where $\displaystyle c_{n}=\sum_{i+j=n} a_{i}b_{j} $) has a radius of convergence R:

(a) $\displaystyle R>min(R_{1},R_{2})$

(c) $\displaystyle max(R_{1},R_{2})<R<\infty$