Problem

6 (10%). Determine whether the following series is convergent or divergent.

$$\lim_{n\to\infty}\sum_{k=1}^{n}\left|\frac{16k^2}{n^3}-\frac{16k}{n^2}+\frac{3}{n}\right|$$

If it is convergent, find its sum. Otherwise, give a reason for your answer.