Harmonic progression (h.p.), Mathematics

Assignment Help:

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.


Related Discussions:- Harmonic progression (h.p.)

Business mathematics, explain how business mathematics in an inbu;it compo...

explain how business mathematics in an inbu;it component of a payroll package

Advantages and disadvantages of decision trees, Advantages of decision tree...

Advantages of decision trees 1. This clearly brings out implicit calculations and assumptions for all to see question and revise 2. This is simple to understand Disadvan

What is the greatest common factor of 24 and 64, What is the greatest commo...

What is the greatest common factor of 24 and 64? List the factors of 24 and 64. The largest factor that they have in common is the greatest common factor. Factors of 24: 1,

Vijay, how to solve trignometric equations more easier?

how to solve trignometric equations more easier?

How much was invested at 12% if the total annual interest, Jackie invested ...

Jackie invested money in two different accounts, one of that earned 12% interest per year and another that earned 15% interest per year. The amount invested at 15% was 100 more tha

PROBABILITY.., Urn A contains 1 white,2 black and 3 red balls;Urn B contain...

Urn A contains 1 white,2 black and 3 red balls;Urn B contains 2 white,1 black and 1 red balls;and Urn C contains 4 white,5 black and 3 red balls.One urn is chosen at random and two

The sum of -4 and a number is equal to -48 what is number, The sum of -4 an...

The sum of -4 and a number is equal to -48. What is the number? Let x = the number. Because sum is a key word for addition, the equation is -4 + x = -48. Add 4 to both sides o

#algebra 2 .., encoded with the matrix -3 -7 and 4 9. what lights up a socc...

encoded with the matrix -3 -7 and 4 9. what lights up a soccer stadium? ecoded message: {-3 - 7} {3 2 } {3 6} {57 127} {52 127} {77 173} {23 51)

Vectors, A 10 m ladder of 150N is placed at an angle 30degrees to a smooth ...

A 10 m ladder of 150N is placed at an angle 30degrees to a smooth wall at point A and the other end (point B) on the ground. Assume that the weight of the ladder acts at its mid po

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd