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.)

Probability transition matrices or brand switching, Define the Probability ...

Define the Probability Transition Matrices or Brand switching.

Solve the linear programming problem using simple method, Solve the followi...

Solve the following Linear Programming Problem using Simple method. Maximize Z= 3x 1 + 2X 2 Subject to the constraints:                  X 1 + X 2 ≤ 4

Equal matrices, Is this given matrices are called equal Matrices?

Is this given matrices are called equal Matrices?

Muptipucation, if 2+2=4 what does two times two epual?

if 2+2=4 what does two times two epual?

Whats this, how do you determine if a graph has direct variation

how do you determine if a graph has direct variation

Articulate reasons and construct arguments, By such interactions children l...

By such interactions children learn to articulate reasons and construct arguments. When a child is exposed to several interactions of this kind, she gradually develops the ability

Find the number of males and females in the village, The population of the ...

The population of the village is 5000.  If in a year, the number of males were to increase by 5% and that of a female by 3% annually, the population would grow to 5202 at the end o

Example for pre-operational stage learning maths, E1) I have a three-year-o...

E1) I have a three-year-old friend. He has a lot of toy cars to play with. Playing with him once, I divided the cars into two sets. One set was more spread out and had 14 cars in i

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