Find the value of `n` so that `(a^(n+1)+b^(n+1))/(a^n+b^n)` may be the geometric mean between `a` and `b`.

Explanation

To find the value of \( n \) such that

\[ \frac{a^{n+1} + b^{n+1}}{a^n + b^n} \]

is the geometric mean of \( a \) and \( b \), we start by recalling that the geometric mean of two numbers \( a \) and \( b \) is given by

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