Let Sn=1⋅(n−1)+2⋅(n−2)+3⋅(n−3)+⋯+(n−1)⋅1, n≥4. The – InterviewSolution

1.	Let Sn=1⋅(n−1)+2⋅(n−2)+3⋅(n−3)+⋯+(n−1)⋅1, n≥4. The sum ∞∑n=4(2Snn!−1(n−2)!) is equal to
Answer» Let $S_{n} = 1 \cdot (n - 1) + 2 \cdot (n - 2) + 3 \cdot (n - 3) + \dots + (n - 1) \cdot 1, n \geq 4.$ The sum $\infty \sum n = 4 (\frac{2 S_{n}}{n!} - \frac{1}{(n - 2)!})$ is equal to

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