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## Homework Statement

Let ## S_k , k = 1,2,3,…,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 value of ##\frac {100^2}{100!} + \sum\limits_{k=1}^{100} | (k^2 - 3k + 1)S_k | ## is

## Homework Equations

Sum of infinite geometric series is a/(1-r) where a is first term and r the common ratio.

## The Attempt at a Solution

Got ## S_k= \frac{1}{(k-1)!}##