# 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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