Can a series be non absolutely convergent at point beyond its radius of absolute convergence?

Question

Let $\sum a_nx^n$ be a series, where $a_n$'s are not necessarily positive & let $R>0$ be its radius of absolute convergence. Then for $x=r>R$, $\sum |a_n|r^n$ will be divergent, but my question is, can the series $\sum a_nr^n$ be convergent.

Please give me few examples.