Series Demystified-1

Algebra Level 3

$\sum_{n=1}^{50} \frac{n^2+3n+1}{n^2+3n+2}$ If the above series can be expressed as $\frac A B$ , where $A$ & $B$ both are coprime positive integers, then find $A+B$ .

Series Demystified-1

This is one of my original Series Demystified problems.