If \(x^2-x + 1= 0\), for what value is the summation of \( \dfrac{x^n}{x^{2n} + 1} \) for natural number \(n\) converge?

**Details and Assumptions**:

\(Converges\) in this sentence is like this:

For some value of \(a\),

\(0.aaaaaaa...\) \(converges\) to \(1\)

\(a+-a+a+-a+a+-a+...\) \(converges\) to \(0\)

\(a+-a+-a+a+a+-a+-a+a+...\) \(converges\) to \(0\).

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