Problem 37 */**

Let S_r for r = 1,2,3, \ldots, 100 denote the sum of the infinite geometric series whose first term is \dfrac {r - 1} {r!} with common ratio \dfrac 1 r.

Evaluate \displaystyle \frac {100^2} {100!} + \sum_{r = 1}^{100} |(r^2 - 3r + 1) S_r|

[originally posted by Felix Felicis on TSR]