Require (\dfrac{a^n+b^n}{a^{n-1}+b^{n-1}}=\sqrt{ab}) (positive G.M.)
Try (n=\dfrac{1}{2}): [ \dfrac{a^{1/2}+b^{1/2}}{a^{-1/2}+b^{-1/2}}=\dfrac{\sqrt{a}+\sqrt{b}}{\dfrac{\sqrt{b}+\sqrt{a}}{\sqrt{ab}}}=\sqrt{ab} ]
Answer: (n=\dfrac{1}{2})
11TH•Mathematics•Sequences And Series•Question 4
Overview
For what value of $n$, $\dfrac{a^n + b^n}{a^{n-1} + b^{n-1}}$ is the positive geometric mean between $a$ and $b$?
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