1. **State the problem:** We need to find the radius of convergence of the power series $$\sum_{n=1}^\infty n x^n$$. 2. **Recall the formula:** The radius of convergence $R$ of a power series $$\sum a_n x^n$$ can be found using the formula $$\frac{1}{R} = \limsup_{n \to \infty} |a_n|^{1/n}$$ or the root test. 3. **Identify coefficients:** Here, the coefficients are $a_n = n$. 4. **Apply the root test:** Calculate $$\limsup_{n \to \infty} |n|^{1/n}$$. 5. **Evaluate the limit:** Since $$\lim_{n \to \infty} n^{1/n} = 1$$, we have $$\limsup_{n \to \infty} |a_n|^{1/n} = 1$$. 6. **Find radius of convergence:** Using $$\frac{1}{R} = 1$$, we get $$R = 1$$. **Final answer:** The radius of convergence of the series $$\sum n x^n$$ is $$\boxed{1}$$.