Mathematics
Let \(A_{1},G_{1}\) and \(H_{1}\) denote the arithmetic, geometric and
harmonic means . respectively of two distinct positive numbers. For
\(n \geq 2\) let \(A_{n - 1}\) and \(H_{n - 1}\) have . arithmetic,
geometric and harmonic means as \(A_{n},G_{n},H_{n}\) respectively
Which of the following statements is correct?
A
\(H_{1} > H_{2} > H_{3} > \ldots\)
B
\(H_{1} < H_{2} < H_{3} < \ldots\)
C
\(H_{1} > H_{3} > H_{5} > \ldots\). and \(H_{2} < H_{4} < H_{6} < \ldots\)
D
\(H_{1} < H_{3} < H_{5} < \ldots\). and \(H_{2} > H_{4} > H_{6} > \ldots\)
Select an option to instantly check whether it is correct or wrong.
