For what value of `n ,\ dot(a^(n+1)+b^(n+1))/(a^n+b^n)` is the arithmetic mean of `a\ a n d\ b ?`

Explanation

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

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

is equal to the arithmetic mean of \( a \) and \( b \), we start by recalling that the arithmetic mean of \( a \) and \( b \) is given by:

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