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.)

Prove that sec2+cosec2 can never be less than 2, Prove that sec 2 θ+cosec 2...

Prove that sec 2 θ+cosec 2 θ can never be less than 2. Ans:    S.T Sec 2 θ + Cosec 2 θ can never be less than 2. If possible let it be less than 2. 1 + Tan 2 θ + 1 + Cot

Theory of meta-games, Theory of Meta-games This theory shows to describ...

Theory of Meta-games This theory shows to describe how most people play non zero sum games concerning a number of persons Prisoner's dilemma is an illustration of this. The

Linear equation, develop any two linear equation which are reducible into l...

develop any two linear equation which are reducible into linear form from our daily life by cross multiplication

what are the coordinates of the vertex , Use the graph of y = x2 - 6x  to ...

Use the graph of y = x2 - 6x  to answer the following: a)         Without solving the equation (or factoring), determine the solutions to the equation  x 2 - 6x = 0  usi

Solve 5x tan (8x ) =3x trig function, Solve 5x tan (8x ) =3x . Solution...

Solve 5x tan (8x ) =3x . Solution : Firstly, before we even begin solving we have to make one thing clear.  DO NOT CANCEL AN x FROM BOTH SIDES!!! Whereas this may appear like

Function to convert a complex number in algebraic form, Go back to the com...

Go back to the complex numbers code in Figures 50 and 51 of your notes. Add code fragments to handle the following: 1. A function for adding two complex numbers given in algeb

Example of elps maths learning, Do you agree with the necessity of the sequ...

Do you agree with the necessity of the sequencing E - L - P - S for learning? If not, then what do you suggest as an alternative path for understanding and internalising mathematic

HELP, WHAT TWO SIX DIDGIT NUMBERS CAN YOU ADD 984,357

WHAT TWO SIX DIDGIT NUMBERS CAN YOU ADD 984,357

Childrens errors are a natural and inevitable part, Childrens errors are a ...

Childrens errors are a natural and inevitable part of their process of learning. In the process of grasping new concepts, children apply their existing understanding, which may

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