Cool summation

Calculus Level 4

Let SkS_{k} ,k=1,2,3,....,100k=1,2,3,....,100, denote the sum of infinite G.P. whose first term is k1k!\frac { k-1 }{ k! } and common ratio is 1k\frac { 1 }{ k }. Then the value of 1002100!+k=1100(k23k+1)Sk\frac { { 100 }^{ 2 } }{ 100! } +\sum _{ k=1 }^{ 100 }{ \left| \left( { k }^{ 2 }-3k+1 \right) S_{k} \right| } is:

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