Sum of an infinite geometric sum

Algebra Level 4

Let A\mathcal{A} be the set of first hundred natural numbers.
A function f(t)f(t) is defined from A\mathcal{A} to R\mathbb{R} which denotes the sum of of infinite geometric series whose first term is t1t!\frac{t-1}{t!} and the common ratio is 1t\frac{1}{t}.

Let S(n)S(n) denote the sum:
S(n)=r=1n(r23r+1)f(r)S(n) = \sum_{r=1}^n | (r^2-3r+1)f(r) |

Find the value of 1002100!+S(100)\frac{100^2}{100!} + S(100).

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