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.)

Abstract Algebra, let R be a (noncommutative) ring. Given that a,b and a+b ...

let R be a (noncommutative) ring. Given that a,b and a+b ? R are all units, prove that a^(-1)+b^(-1) is a unit

Solving ratios, you are in charge of making punch for an upcoming dance. th...

you are in charge of making punch for an upcoming dance. the punch recipe makes 5 cups of punch by making 3 cups of cranberry juice with 2 cups of apple juice. What is the ratio of

Obligatory application and interpretation problem, Obligatory application/i...

Obligatory application/interpretation problem : Next, we need to do our obligatory application/interpretation problem so we don't forget about them. Example : Assume that the

Explain histogramsin details, Explain Histogramsin details? Another way...

Explain Histogramsin details? Another way to display frequencies is by using a histogram. The following is an example of a histogram using the data from the previous example:

Geometric interpretation of the cross product, Geometric Interpretation of ...

Geometric Interpretation of the Cross Product There is as well a geometric interpretation of the cross product.  Firstly we will let θ be the angle in between the two vectors a

Describe order of operations with example, Describe Order of Operations wit...

Describe Order of Operations with example? The order of operations is a set of rules that describe the order in which math operations are done. Try doing this math problem:

Area, area of r=asin3x

area of r=asin3x

Total linear attenuation, Consider the task of identifying a 1 cm thick bre...

Consider the task of identifying a 1 cm thick breast cancer that is embedded inside a 4.2 cm thick fibroglandular breast as depicted in Fig. The cancerous tumor has a cross

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