Let \( S_{k}, k=1,2, \ldots, 100 \), denote the sum of the infinite geometric series whose first...

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Let \( S_{k}, k=1,2, \ldots, 100 \), denote the sum of the infinite geometric series whose first term is \( \frac{k-1}{k !} \) and the common ratio is \( \frac{1}{k} \), then the value of \( \frac{100^{2}}{100 !}+\sum_{k=1}^{100}\left|\left(k^{2}-3 k+1\right) S_{k}\right| \) is
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