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
\(A_{1} > A_{2} > A_{3} > \ldots\)
B
\(A_{1} < A_{2} < A_{3} < \ldots\)
C
\(A_{1} > A_{3} > A_{5} > \ldots\). and \(A_{2} < A_{4} < A_{6} < \ldots\)
D
\(A_{1} < A_{3} < A_{5} < \ldots\). and \(A_{2} > A_{4} > A_{6} > \ldots\)
Select an option to instantly check whether it is correct or wrong.
