Series Demystified 9

Algebra Level 4

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

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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