Question 3
$a$, $b$, $c$, $d$ are integers with $ad \neq bc$. Show that $\frac{1}{(ax+b)(cx+d)}$ can be written in the form $\frac{r}{ax+b} + \frac{s}{cx+d}$. Find the sum
$$
\frac{1}{1 \cdot 4} + \frac{1}{4 \cdot 7} + \frac{1}{7 \cdot 10} + \dots + \frac{1}{2998 \cdot 3001}
$$
$$
\frac{1}{1 \cdot 4} + \frac{1}{4 \cdot 7} + \frac{1}{7 \cdot 10} + \dots + \frac{1}{2998 \cdot 3001}
$$