An algebra problem by Pankaj Joshi

Algebra Level 5

Let \(S_k\) \((k = 1,2,3,...,100)\) denote the sum of infinite Geometric Progression whose first term is \(\dfrac {k-1}{k!}\) and the common ratio is \(\dfrac{1}{k}\). Then find the value of \(\dfrac{100^2}{100!}\) + \(\sum_{k=1}^{100} \lvert(k^2 - 3k +1) . S_k \rvert\)

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