# 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:

×