Series Demystified 6

Algebra Level 4

\[ \large \sum_{n=1}^{48} \log \left ( \frac {n}{n^2+3n+2} \right )\]

If the summation above equals to \(S\), then \(S+\log(49!)=-\log P.\) Find the value of \(P\).

This is one of my original Series Demystified problems.
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