Consecutively different

Algebra Level 5

\[ \begin{eqnarray} S_1 &=& 1 + \dfrac{1}{4} + \dfrac{1\times 4}{4\times 8} + \dfrac{1\times 4\times 7}{4\times 8\times 12} + \dfrac{1\times 4\times 7\times 10}{4\times 8\times 12\times 16} + \ldots \\ S_2 &=& 1 + \dfrac{2}{6} + \dfrac{2\times 5}{6\times 12} + \dfrac{2\times 5\times 8}{6\times 12\times 18} + \dfrac{2\times 5\times 8\times 11}{6\times 12\times 18\times 24} + \ldots \\ \end{eqnarray} \]

Let us define two infinite series, \(S_1\) and \(S_2\) as above.

What is the relationship between \(S_1 \) and \(S_2 \)?

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