JEE Advance - Mathematics (1991 - No. 10)
Let p be the first of the n arithmetic means between two numbers and q the first of n harmonic means between the same numbers. Show that q does not lie between p and $$\,{\left( {{{n + 1} \over {n - 1}}} \right)^2}\,p$$.
The statement is always true.
The statement is true only when the two numbers are equal.
The statement is false and q always lies between p and $$\left( \frac{n+1}{n-1} \right)^2 p$$.
The statement's validity depends on the specific values of the two numbers and n.
The question is ambiguous and needs further clarification.