# $$Convergence$$

Calculus Level 3

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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