- For each of these power series, decide for which values of \(x\) the series converges. This is the same as asking about the interval/radius of convergence of the series. \[ \sum_{n=1}^{\infty} \frac{(x-5)^n}{n} \qquad \qquad \qquad \sum_{n=1}^{\infty} n! x^n \qquad \qquad \qquad \sum_{n=1}^{\infty} \frac{x^n}{(2n)!} \] \[ \sum_{n=0}^{\infty} \frac{(-1)^n x^n}{\sqrt{n+4}} \qquad \qquad \qquad \sum_{n=0}^{\infty} \frac{2n (x+3)^n}{5^{n-1}} \qquad \qquad \qquad \sum_{n=1}^{\infty} \frac{x^{2n}}{n!} \]