If frac{a^{n + 1} + b^{n + 1}}{a^n + b^n} is | vedclass

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(B) The harmonic mean $(HM)$ of two numbers $a$ and $b$ is given by $\frac{2ab}{a + b}$.Given that $\frac{a^{n + 1} + b^{n + 1}}{a^n + b^n} = \frac{2a

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$-1$

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(B) The harmonic mean $(HM)$ of two numbers $a$ and $b$ is given by $\frac{2ab}{a + b}$.Given that $\frac{a^{n + 1} + b^{n + 1}}{a^n + b^n} = \frac{2ab}{a + b}$.Cross-multiplying,we get $(a^{n + 1} + b^{n + 1})(a + b) = 2ab(a^n + b^n)$.Expanding both sides: $a^{n + 2} + a^{n + 1}b + ab^{n + 1} + b^{n + 2} = 2a^{n + 1}b + 2ab^{n + 1}$.Rearranging the terms: $a^{n + 2} + b^{n + 2} = a^{n + 1}b + ab^{n + 1}$.$a^{n + 1}(a - b) - b^{n + 1}(a - b) = 0$.$(a^{n + 1} - b^{n + 1})(a - b) = 0$.Since $a 
eq b$,we must have $a^{n + 1} = b^{n + 1}$.This implies $(\frac{a}{b})^{n + 1} = 1 = (\frac{a}{b})^0$.Therefore,$n + 1 = 0$,which gives $n = -1$.

If $\frac{a^{n + 1} + b^{n + 1}}{a^n + b^n}$ is the harmonic mean between $a$ and $b$,then the value of $n$ is

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