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.)

Transforming the base of logarithms, Suppose that we know the logarit...

Suppose that we know the logarithms of all numbers which are expressed to base 'a' and we are required to find the logarithms of all these numbers to base 'b'. We

Parenteral calculations, 850ml is to be administered to a person over 8 hou...

850ml is to be administered to a person over 8 hours using a drop factor of 20 drops/ml what is the flow rate in gtts/min ?

Fractions, what is the lowest term of 11/121

what is the lowest term of 11/121

Venn diagram, A venn diagram is a pictorial representation of the sam...

A venn diagram is a pictorial representation of the sample space of an experiment. It is usually drawn as a rectangular figure representing the sample space and it cont

How much will it have depreciated after 2 years, The value of a computer is...

The value of a computer is depreciated over ?ve years for tax reasons (meaning that at the end of ?ve years, the computer is worth $0). If a business paid $2,100 for a computer, ho

Imaginay Number, how to solve imaginary number such as like (-3v-5)² ?? Can...

how to solve imaginary number such as like (-3v-5)² ?? Can I cancel the radical sign and the power of two ? and square the -3 and times to -5 ? hope you will answer this :) thanks

Complex numbers, find the modulus Z=(2-i)(5+i12)/(1+i2)^3

find the modulus Z=(2-i)(5+i12)/(1+i2)^3

Solve the second order differential equations, Solve the subsequent IVP ...

Solve the subsequent IVP Y'' - 9 y = 0, y(0) = 2, y'(0) = -1 Solution First, the two functions  y (t ) = e 3t  and  y(t ) = e -3t That is "nice enough" for us to

Define regression, Define regression. The main reason of curve fitting ...

Define regression. The main reason of curve fitting is to estimate one of the variables (the dependent variable) from the other (the independent variable). The procedure of est

Find the sum of all natural numbers, Find the sum of all natural numbers am...

Find the sum of all natural numbers amongst first one thousand numbers which are neither divisible 2 or by 5 Ans:    Sum of all natural numbers in first 1000 integers which ar

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