Question

If (a^n+1+b^n+1)/a^nb^n is the AM between a and b.Find the value of n.

Answer 1

From the given AM between a and b is

(aⁿ + bⁿ)/(aⁿ⁻¹ + bⁿ⁻¹)

AM of a and b is (a+b)/2

(aⁿ + bⁿ)/(aⁿ⁻¹ + bⁿ⁻¹) = (a+b)/2

Cross multiply....

2(aⁿ + bⁿ) = (a+b)(aⁿ⁻¹ + bⁿ⁻¹)

Multiply inside brackets...

2aⁿ + 2bⁿ = a.aⁿ⁻¹ + a.bⁿ⁻¹ + b.aⁿ⁻¹ + b.bⁿ⁻¹

aⁿ + bⁿ = a.bⁿ⁻¹ + b.aⁿ⁻¹

aⁿ - b.aⁿ⁻¹ = a.bⁿ⁻¹ - bⁿ

aⁿ⁻¹ ( a - b) = bⁿ⁻¹ ( a - b)

aⁿ⁻¹/bⁿ⁻¹ = 1

(a/b)ⁿ⁻¹ = (a/b)⁰

n - 1 = 0

n = 1

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Answer 2

Answer:

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