$I f \frac{a^{n} + b^{n}}{a^{n - 1} + b^{n - 1}} i s t h e A . M . b e t w e e n a a n d b, t h e n f i n d t h e v a l u e o f n .$

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Solution

$a^{n +} = b^{n - 1} \frac{a^{n - 1}}{b^{n - 1}} = 1 {(\frac{a}{b})}^{n - 1} = 1 i . e ., n - 1 = 0 n = 1 a = b \frac{a}{b} = 1 {(\frac{a}{b})}^{0} = 1 n = 0$

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