An algebra problem by Manish Dash

Let ${ S }_{ k }\quad =\quad k\quad =\quad 1,2,........,100$ , 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 the value of $\frac { { 100 }^{ 2 } }{ 100! } \quad +\quad \sum _{ k=1 }^{ 100 } \left| ({ k }^{ 2 }-3k+1){ S }_{ k } \right|$ is:

Please post the solution.