# Determining convergence/ divergence of $\sum_{n=0}^\infty \frac{n}{(4n-3)(4n-1)}$

I am having a problem with determining wether this series is convergent or divergent:

$$\sum\limits_{n=0}^\infty \frac{n}{(4n-3)(4n-1)}$$

I just started the chapter on series and we've learned various convergence tests.

The terms don't go to $0$ fast enough for convergence.
Note that for $n\ge 1$, the $n$-th term is $\gt \dfrac{n}{(4n)(4n)}$, that is, $\gt \dfrac{1}{16}\cdot \dfrac{1}{n}$.