Question 15
The sum
$$
\sum_{k=1}^{\infty} \frac{1}{k^3 + 6k^2 + 8k}
$$
can be expressed as $\dfrac{a}{b},$ where $a$ and $b$ are relatively prime positive integers. What is $a + b?$
$$
\sum_{k=1}^{\infty} \frac{1}{k^3 + 6k^2 + 8k}
$$
can be expressed as $\dfrac{a}{b},$ where $a$ and $b$ are relatively prime positive integers. What is $a + b?$