# 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.

×