Series Demystified 6

Algebra Level 4

n=148log(nn2+3n+2) \large \sum_{n=1}^{48} \log \left ( \frac {n}{n^2+3n+2} \right )

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

This is one of my original Series Demystified problems.
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