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.)

Calculate the number-average and weight-average molar mass, Three mixtures ...

Three mixtures were prepared with very narrow molar mass distribution polyisoprenesamples with molar masses of 8000, 25,000, and 100,000 as indicated below. (a) Equal numbers of

Multiplication of two unlike terms with opposite signs, The product on mult...

The product on multiplying - 4bc with 2a is - 8abc. That is, a term with minus sign multiplied with a term having a positive term gives a product which has a minus sign. On the

Loan amortisation problem, On 30 June 2012 Bill purchase a home by taking o...

On 30 June 2012 Bill purchase a home by taking out a 30 year mortgage of $600,000 at 6% interest per annum, compounded months. Repayments are made at the end of each month. (a) Cal

Algebra, If a^n+1 + b^n+1/a^n + b^n is the arithmetic mean of a and b then ...

If a^n+1 + b^n+1/a^n + b^n is the arithmetic mean of a and b then find n. Answer:Arithmatic mean of a,b is =(a+b)/2  from the problem (a+b)/2=(a^n+1 +b ^n+1)/(a^n+b^n)  then (a+

Sequencing., how to select out time for m2

how to select out time for m2

Non zero sum games- game theory, Non Zero Sum Games Recently there was ...

Non Zero Sum Games Recently there was no satisfactory theory either to describe how people should play non-zero games or to explain how they actually play that game Nigel Ho

Find the length of the boundary and the area of the shaded, The boundary of...

The boundary of the shaded portion in the adjoining figure consists of our half-circles and two quarter-circles.  Find the length of the boundary and the area of the shaded portion

The hurwiz method, The Hurwiz method Hurwiz method was the concept of c...

The Hurwiz method Hurwiz method was the concept of coefficient of optimism or pessimism introduced by L. Hurwicz. The decision maker takes into account both the minimum and max

Math, i have problems with math and my teacher said that i am still progres...

i have problems with math and my teacher said that i am still progressing in math

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