Suppose that the power series $$\sum\_{n=1}^\infty a\_nx^n$$ has radius of convergence $R$. Then the power series $$\sum\_{n=1}^\infty na\_nx^{n-1}$$ diverges if $|x|>R$.

**Attempt:** I can show that $\sum\_{n=1}^\infty |na\_nx^{n-1}|$ diverges by comparison test, but how do I show that $\sum\_{n=1}^\infty na\_nx^{n-1}$ diverges also?