## POTW #10 - March 3, 2024

#### Contributed by: asf1re

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#### Difficulty: 9

#### This problem is tagged with potw, potw2024.

**MCR Problem of the Week, March 3, 2024 Edition**

Let $S_n = 1 \cdot (n-1) + 2 \cdot (n-2) + 3 \cdot (n-3) + \cdots + (n-1) \cdot 1, \quad n \geq 4.$

Then find the value of $\left\lceil\sum_{n=4}^{\infty} \left( 2 \frac{S_n}{n!} - \frac{1}{(n-2)!} \right)\right\rceil$

This problem was borrowed from byjus.com.

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