Cool summation

Calculus Level 4

Let $S_{k}$ , $k=1,2,3,....,100$ , denote the sum of infinite G.P. whose first term is $\frac { k-1 }{ k! }$ and common ratio is $\frac { 1 }{ k }$ . Then the value of $\frac { { 100 }^{ 2 } }{ 100! } +\sum _{ k=1 }^{ 100 }{ \left| \left( { k }^{ 2 }-3k+1 \right) S_{k} \right| }$ is: