Harmonic progression (h.p.), Mathematics

Three quantities a, b and c are said to be in harmonic progression if,

2192_harmonic progresssion.png

In this case we observe that we have to consider three terms in order to conclude whether they are in harmonic progression or not.

An important proposition in this case is that the reciprocal of quantities in harmonical progression are in arithmetical progression. Let us understand this by considering three quantities a, b and c. By definition, if a, b and c are in harmonic progression then they satisfy the condition that

2192_harmonic progresssion.png

By cross multiplying, we obtain

                   a(b - c) = c(a - b)

That is,      ab - ac = ac - bc  

Dividing each of these terms by abc, we have

972_harmonic progression.png

This can be written as

722_harmonic progression1.png

Canceling the common terms, we have

378_harmonic progression2.png

This gives us the common difference between the reciprocal terms of a, b and c. This also proves our proposition.

Posted Date: 9/13/2012 4:43:42 AM | Location : United States







Related Discussions:- Harmonic progression (h.p.), Assignment Help, Ask Question on Harmonic progression (h.p.), Get Answer, Expert's Help, Harmonic progression (h.p.) Discussions

Write discussion on Harmonic progression (h.p.)
Your posts are moderated
Related Questions
Two  ships  are  sailing  in  the  sea  on  either  side  of  a  lighthouse;  the  angles  of depression of two ships as observed from the top of the lighthouse are 600  and 450 re

Product Rule: (f g)′ = f ′ g + f g′ As with above the Power Rule, so the Product Rule can be proved either through using the definition of the derivative or this can be proved

What does the abbreviation ''GSA'' mean?

Chelsea has been facing some financial problems which even caused her daily expenses for food, at the same time, she hasn''t receive the money from the bank loan yet. Therefore, sh

Frederick bought six books which cost d dollars each. What is the total cost of the books? Frederick would multiply the number of books, 6, through how much each one costs, d.

A function is an equation for which any x which can be plugged into the equation will yield accurately one y out of the equation. There it is. i.e. the definition of functions w

Extreme Value Theorem : Assume that f ( x ) is continuous on the interval [a,b] then there are two numbers a ≤ c, d ≤ b so that f (c ) is an absolute maximum for the function and

Justin weighed 8 lb 12 oz while he was born. At his two-week check-up, he had gained 8 ounces. What was his weight within pounds and ounces? There are 16 ounces within a pound.

How did the teacher get 30 + 12 + 1.5 for the equation of volume of rectangular prism measuring L=14.4, W= 3, and H= 5? Formula given was V= Bh. My answer was 43.5.14.5 x 3.

In the adjoining figure a dart is thrown at the dart board and lands in the interior of the circle. What is the probability that the dart will land in the shaded region. A