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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