5. (10%) Given the power series \( \sum_{n=1}^{\infty} \frac{1}{2 \cdot 4 \cdot 8 \cdots (2n)} x^n \), (a) find the series' radius and interval of convergence. For what values of \( x \) does the series converge (b) absolutely, (c) conditionally?
5. (10%) Given the power series \( \sum_{n=1}^{\infty} \frac{1}{2 \cdot 4 \cdot 8 \cdots (2n)} x^n \), (a) find the series' radius and interval of convergence. For what values of \( x \) does the series converge (b) absolutely, (c) conditionally?