For what value of m is frac{a^{m+1}+b^{m+1}}{ | vedclass

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(B) The arithmetic mean of $a$ and $b$ is given by $\frac{a+b}{2}$.Given that $\frac{a^{m+1}+b^{m+1}}{a^m+b^m} = \frac{a+b}{2}$.Cross-multiplying the

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$0$

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(B) The arithmetic mean of $a$ and $b$ is given by $\frac{a+b}{2}$.Given that $\frac{a^{m+1}+b^{m+1}}{a^m+b^m} = \frac{a+b}{2}$.Cross-multiplying the terms, we get:$2(a^{m+1} + b^{m+1}) = (a+b)(a^m + b^m)$$2a^{m+1} + 2b^{m+1} = a^{m+1} + ab^m + ba^m + b^{m+1}$Subtracting $a^{m+1} + b^{m+1}$ from both sides:$a^{m+1} + b^{m+1} = ab^m + ba^m$$a^{m+1} - ba^m = ab^m - b^{m+1}$$a^m(a - b) = b^m(a - b)$If $a 
eq b$, we can divide by $(a - b)$:$a^m = b^m$$\left(\frac{a}{b}ight)^m = 1$Since $1 = (\frac{a}{b})^0$, we have $m = 0$.

For what value of $m$ is $\frac{a^{m+1}+b^{m+1}}{a^{m}+b^{m}}$ the arithmetic mean of $a$ and $b$?

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