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Algebra Level 3

Let \(S_{1},S_{2},S_{3}\) denote the sums of the first \(n\) positive integers, their squares, and their cubes respectively. Find

\[ \frac{S_{3}(1+8S_{1})}{(S_{2})^{2}} .\]


You can try my other Sequences And Series problems by clicking here : Part II and here : Part I.
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