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# Find the value of $n$ so that $\large\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$ may be the geometric mean between $a$ and $b$.

$\begin{array}{1 1} \large\frac{1}{2} \\ \large\frac{-1}{2} \\ 1\\ -1\end{array}$