Algebric Sets

Algebra Level 4

{1,2},{4,5,6},{9,10,11,12},{16,17,18,19,20}, \{1,2\} , \{ 4,5,6 \} , \{9,10,11,12\} , \{16,17,18,19,20\} , \ldots

The first nn positive integers are partitioned into sets as described above.

Let SnS_{n} be the sum of the elements of the set at nthn^{\text{th}} position. Find the value of 3S50S51S50.\sqrt{3} \dfrac{S_{50}}{\sqrt{S_{51}-S_{50}}}.

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