Let S(k), where k = 1,2,....,100, denote...

Let `S_(k)`, where `k = 1,2`,....,100, denotes the sum of the infinite geometric series whose first term is `k.(k -1)/(k!)` and the common ratio is `(1)/(k)`. Then, the value of `(100^(2))/(100!) +sum_(k=2)^(100) | (k^(2) - 3k +1) S_(k)|` is....

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