Sequence and Series 2

Calculus Level pending

\[\mathfrak{B}=\dfrac{1^2}{2!}+\dfrac{2^2}{3!}+\dfrac{3^2}{4!}+\ldots = \displaystyle \sum^{\infty}_{n=1}\dfrac{n^2}{(n+1)!}\]

Find \(\lceil \mathfrak{B} \rceil\).

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