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

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(B) The $A.M.$ of $a$ and $b$ is given by $\frac{a+b}{2}$.According to the given condition:$\frac{a+b}{2} = \frac{a^{n}+b^{n}}{a^{n-1}+b^{n-1}}$Cross-

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$1$

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(B) The $A.M.$ of $a$ and $b$ is given by $\frac{a+b}{2}$.According to the given condition:$\frac{a+b}{2} = \frac{a^{n}+b^{n}}{a^{n-1}+b^{n-1}}$Cross-multiplying,we get:$(a+b)(a^{n-1}+b^{n-1}) = 2(a^{n}+b^{n})$Expanding the left side:$a^{n} + ab^{n-1} + ba^{n-1} + b^{n} = 2a^{n} + 2b^{n}$Rearranging the terms:$ab^{n-1} + a^{n-1}b = a^{n} + b^{n}$Grouping terms:$ab^{n-1} - b^{n} = a^{n} - a^{n-1}b$$b^{n-1}(a-b) = a^{n-1}(a-b)$Assuming $a 
eq b$,we divide by $(a-b)$:$b^{n-1} = a^{n-1}$$\left(\frac{a}{b}ight)^{n-1} = 1 = \left(\frac{a}{b}ight)^{0}$Equating the exponents:$n-1 = 0$$n = 1$

If $\frac{a^{n}+b^{n}}{a^{n-1}+b^{n-1}}$ is the $A.M.$ between $a$ and $b,$ then find the value of $n$.

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