Question

If \(a, b\) and \(c\) are in HP, then for any \(n \in \mathbb{N}\), which one of the following is true?

• A. \(a^n + c^n<2b^n\)
• B. \(a^n + c^n>2b^n\)
• C. \(a^n + c^n = 2b^n\)
• D. None of these

Hint:

HP $\Rightarrow$ reciprocals in AP $\Rightarrow$ middle term smaller $\Rightarrow$ use convexity for powers.

Answer 1

The Correct Option is B