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.)

Write radicals in exponent form, Write each of the given radicals in expone...

Write each of the given radicals in exponent form. Solution As illustrated in the last two parts of this example we have to be careful with parenthesis.  While we

Factoring quadratics of the form x2 + bx + c, Factoring quadratics of the f...

Factoring quadratics of the form x 2 + bx + c ? This tutorial will help you factor quadratics that look something like this: x 2 + 7x + 12 (Positive coefficients; no lea

Trignometry, i have to get 10 points in 10th class

i have to get 10 points in 10th class

Algebra problem solving , A rectangles lenth is (x+4) and width is (x+3).By...

A rectangles lenth is (x+4) and width is (x+3).By adding binomials give its perimiter

Geometry, How do you solve (17+w)^2 + w^2 = (25+w)^2

How do you solve (17+w)^2 + w^2 = (25+w)^2

ConnectEd, How do I increase and decrease tax and sales

How do I increase and decrease tax and sales

Pairs of straight lines, The equation ax2 + 2hxy + by2 =0 represents a pair...

The equation ax2 + 2hxy + by2 =0 represents a pair of straight lines passing through the origin and its angle is tan q = ±2root under h2-ab/(a+b) and even the eqn ax2+2hxy+by2+2gx+

Interval of convergence - sequences and series, Interval of Convergence ...

Interval of Convergence After that secondly, the interval of all x's, involving the endpoints if need be, for which the power series converges is termed as the interval of conv

Quadratic equation assignment, what is number of quadratic equation that ar...

what is number of quadratic equation that are unchanged by squaring their roots is There are four such cases x 2   =0 root 0 (x-1) 2 =0  root 1 x(x+1)=0  roots  0 and 1

How to multiplying rational expressions, how to Multiplying Rational Expres...

how to Multiplying Rational Expressions ? To multiply fractions, or rational expressions, you must multiply the numerators and then multiply the denominators. Here's how it is

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