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Let S, P and R denote, respectively, the sum, product, and sum of the reciprocals of n terms of an increasing geometric progression. If Sⁿ = Rⁿ · P^k, then the value of k is

1. 1
2. 2
3. 3
4. None of these

Correct answer: 2

Solution

For an n-term GP, S/R = a^2 r^(n-1) and P^2 = a^(2n) r^(n(n-1)) = (a^2 r^(n-1))^n. Hence (S/R)^n = P^2, i.e. S^n = R^n P^2, so k = 2.

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