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$\large \displaystyle \sum_{n=1}^{48} \dfrac{1+n+n^2}{(n^2 + n)(n+1)!}$

If the above summation can be expressed as $S$, find $\dfrac{1}{\sqrt{49!\left(\lceil S \rceil - S\right)}}$.

Note:

$\lceil . \rceil$ is the ceiling function.

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