alleryThe value of $n$ for which $\dfrac{a^{n+1}+b^{n+1}}{a^{n}+b^{n}}$ is the geometric mean of $a$ and $b$ is:
A$\tfrac{1}{2}$
B$-\tfrac{1}{2}$
C$1$
D$0$
Answer & Solution
Correct answer: B. $-\tfrac{1}{2}$
Setting the expression equal to √(ab) and simplifying gives a^{n+1}+b^{n+1} = √(ab)(a^n+b^n)
this holds for n = −1/2.
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