Consider the infinite series
$$ \begin{array}{l} \text { (P) }: \sum_{n=2}^{\infty} \frac{1}{(n \log n)^{1 / n}} \\
\text { (Q): } \sum_{n=1}^{\infty} \frac{n^{n}}{(2 n)!}
\end{array}$$
Then which one of the following statements is correct?
- Series $(P)$ and $(Q)$ both converge
- Series $(P)$ converges and series $(Q)$ diverges
- Series $(P)$ and $(Q)$ both diverge
- Series $(P)$ diverges and series $(Q)$ converges
