2.8.12 Power series

Problem: Find the domain of convergence of the power series. 1) \( \sum_{n=1}^{\infty} \frac{e^{-n} x^{n}}{\sqrt{n^{3}+1}} \), 2) \( \sum_{n=1}^{\infty} \frac{n^{n}(x+1)^{n}}{n !} \).