Answer
Absolutely Convergent
Work Step by Step
By the Ratio Test:
$\lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right| < 1$
$\lim_{{n \to \infty}} \left| \frac{a_{n+1}}{a_n} \right| = \lim_{{n \to \infty}} \left| \frac{\frac{\pi^{2(n+1)}}{2(n+1)!}}{\frac{\pi^{2n}}{2n!}} \right|= \lim_{{n \to \infty}} \left| \frac{\pi^{2n+2}}{2(n+1)!} \cdot \frac{2n!}{\pi^{2n}} \right| = \lim_{{n \to \infty}} \left| \frac{\pi^{2}}{(2n+2)(2n+1)} \right|=0$
By the Ratio Test the series Converges Absolutely.
