Question

How do I prove that the harmonic mean of a and b is a true average? that is to say a≤H(a,b)≤b if a≤b

Answer 1

It's easy to prove when assuming that both a and b are positive numbers but it's difficult to find a sleek solution which takes all scenarios into account. what if a is positive and b negative or vice versa or if both of them are negative. Is there any method which will account for all of that at once.