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 \(A+B\).

This is one of my original Series Demystified problems.
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