Series Demystified 9

Algebra Level 4

n=1481+n+n2(n2+n)(n+1)!\large \displaystyle \sum_{n=1}^{48} \dfrac{1+n+n^2}{(n^2 + n)(n+1)!}

If the above summation can be expressed as SS, find 149!(SS)\dfrac{1}{\sqrt{49!\left(\lceil S \rceil - S\right)}} .

Note:

.\lceil . \rceil is the ceiling function.

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