If the nth term of a harmonic progression is given by 1/(1/n + 1/m), what does t
Practice Questions
Q1
If the nth term of a harmonic progression is given by 1/(1/n + 1/m), what does this represent?
The average of n and m
The product of n and m
The sum of n and m
The difference of n and m
Questions & Step-by-Step Solutions
If the nth term of a harmonic progression is given by 1/(1/n + 1/m), what does this represent?
Step 1: Understand what a harmonic progression (HP) is. It is a sequence of numbers where the reciprocals of the numbers form an arithmetic progression (AP).
Step 2: Recall that the nth term of a harmonic progression can be expressed in terms of the harmonic mean of two numbers.
Step 3: The formula for the harmonic mean of two numbers n and m is given by 1 / (1/n + 1/m).
Step 4: Recognize that the expression 1/(1/n + 1/m) represents the nth term of the harmonic progression.
Step 5: Conclude that this means the nth term is the harmonic mean of the two numbers n and m.
Harmonic Progression – A sequence of numbers is in harmonic progression if the reciprocals of the terms form an arithmetic progression.
Harmonic Mean – The harmonic mean of two numbers n and m is calculated as 2/(1/n + 1/m), which is related to the nth term of a harmonic progression.
