Set of sets

Algebra Level 3

If the set of positive integers is partitioned into subsets \({ S }_{ 1 }=\left\{ 1 \right\} ,{ S }_{ 2 }=\left\{ 2,3 \right\} ,{ S }_{ 3 }=\left\{ 4,5,6 \right\} , \ldots,\) then what is the sum of the members in \({ S }_{ 50 }?\)

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