The answer is not 1

Calculus Level 4

If x1xx2\displaystyle \frac{x}{1-x-x^2} can be expressed in the form n=1anxn\displaystyle \sum_{n=1}^\infty a_n x^n for a certain subset of reals such that aiR\displaystyle a_i \in \mathbb{R} and iN,\forall i \in \mathbb{N} , what is the value of limnan+1an?\displaystyle{\lim_{n \to \infty} \frac{a_{n+1}}{a_n}}?

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