4. (10%) Consider the infinite series $\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^2}$, where $a > 0$. Find the necessary and sufficient condition of $a$ such that the series is convergent, or argue that no such condition exists.
4. (10%) Consider the infinite series $\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^2}$, where $a > 0$. Find the necessary and sufficient condition of $a$ such that the series is convergent, or argue that no such condition exists.