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Let SkS_{k}Sk ,k=1,2,3,....,100k=1,2,3,....,100k=1,2,3,....,100, denote the sum of infinite G.P. whose first term is k−1k!\frac { k-1 }{ k! }k!k−1 and common ratio is 1k\frac { 1 }{ k }k1. Then the value of 1002100!+∑k=1100∣(k2−3k+1)Sk∣\frac { { 100 }^{ 2 } }{ 100! } +\sum _{ k=1 }^{ 100 }{ \left| \left( { k }^{ 2 }-3k+1 \right) S_{k} \right| }100!1002+∑k=1100∣∣(k2−3k+1)Sk∣∣ is:
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