To infinity and beyond

Calculus Level 3

\[ \dfrac{1}{1 + 1^2 + 1^4} + \dfrac{2}{ 1 + 2^2 + 2^4} + \dfrac{3}{1 + 3^2 + 3^4} + \ldots + \dfrac{n}{1 + n^2 + n^4} \]

Let \(S_n\) denote summation above. Evaluate \( \displaystyle \lim_{n \to \infty} S_n \).

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