Spooky + scary = Summation

Algebra Level 5

If \(S_{k}, (k=1,2,3 \cdots ,100),\) denotes the infinite geometric progression sum, whose first term is \(\dfrac{k - 1}{k!}\) and common ratio is \(\dfrac{1}{k}\) , then find \[ \large \dfrac{(100)^{2}}{100!} + \displaystyle \sum_{k=2}^{100} | (k^{2} - 3 k + 1) \cdot S_{k} | \]

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