2.10.95 Number series

Condition: For a given number series; a) write its first 5 terms, b) justify the convergence, c) find the sum using the well-known Maclaurin expansions of elementary functions. \[ \sum_{n=1}^{\infty} \frac{(-1)^{n} \pi^{2 n}}{(2 n) ! \cdot 16^{n}} \]