In class we talked about power series and the radius of convergence. After that we talked about the addition of two power series with radii of convergence respectively Ra and Rb. Now the theorem says that Σ(an+bn)x^n has a radius of convergence R>=min{Ra,Rb}. Finally, there are examples of such power series where R is strictly greater than min{Ra,Rb}. My question is: which example of such power series?

Finding such example is quite important, it is asked in my book with exclamation marks..

Thanks in advance,

Leslon