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.)

Differential equation (dy/dx) +x^2 = x^2*e^(3y), The general solution of th...

The general solution of the differential equation (dy/dx) +x^2 = x^2*e^(3y). Solution)(dy/dx) +x^2 = x^2*e^(3y) dy/dx=x 2 (e 3y -1) x 2 dx=dy/(e 3y -1) this is an elementar

Calculate the mean, Calculate the mean, variance & standard deviation of th...

Calculate the mean, variance & standard deviation of the number of heads in a simultaneous toss of three coins.     SOLUTION:    Let X denotes the number of heads in a simu

Converting mixed numbers to improper fractions, Q. Converting Mixed Numbers...

Q. Converting Mixed Numbers to Improper Fractions? Ans. Converting a mixed number to an improper fraction is easy. A single multiplication, and then a single addition:

Please help me solve these Problems step by step, What angle (to the neares...

What angle (to the nearest degree) corresponds to the cos 0.6 or what is cos-1(0.6)? (Note: Use Appendix I) What angle (to the nearest degree) corresponds to the sin 0.6 or what

Brian 100-yard dash time was 2.68 what is the school record, Brian's 100-ya...

Brian's 100-yard dash time was 2.68 seconds more than one school record. Brian's time was 13.4 seconds. What is the school record? The school record is less than Brian's time.

In the terms of x, The length of Kara's rectangular patio can be expressed ...

The length of Kara's rectangular patio can be expressed as 2x - 1 and the width can be expressed as x + 6. In the terms of x, what is the area of her patio? Since the area of a

Toni tiger, Application Practice Answer the following questions. Use Equat...

Application Practice Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save this file to your hard drive by selecting Sav

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