Algebra
# Partial Fractions

$\large \displaystyle \sum_{n = 1}^{\infty} \dfrac {1}{n^2 + 3n + 2} = \ ?$

Consider the following pattern:

$\begin{aligned} \frac{1}{1\times 2} & = \frac{1}{1} - \frac{1}{2} \\ & \\ \frac{1}{2\times 3} & = \frac{1}{2} - \frac{1}{3} \\ & \\ \frac{1}{3\times 4} & = \frac{1}{3} - \frac{1}{4} \\ \vdots & \end{aligned}$

Following the pattern above, if $\displaystyle \frac{1}{11\times 12} = \frac{1}{a} - \frac{1}{b},$ what are the values of $a$ and $b$?