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.)

Fraction, One day it snowed 3 and 3/8 inches in Altoona and 3.45 inches in ...

One day it snowed 3 and 3/8 inches in Altoona and 3.45 inches in Bethlehem. Which city received less snow that day.

Explain why f must be a di?erentiable function, Let f : R 3 → R be de?ned ...

Let f : R 3 → R be de?ned by:                                        f(x, y, z) = xy 2 + x 3 z 4 + y 5 z 6 a) Compute ~ ∇f(x, y, z) , and evaluate ~ ∇f(2, 1, 1) . b) Brie?y

What is the total balance of an account after 18 months, A certain bank pay...

A certain bank pays 3.4% interest per year for a certificate of deposit, or CD. What is the total balance of an account after 18 months along with an initial deposit of $1,250?

Calculate the regular monthly payments, A washing machine, cash price $ 850...

A washing machine, cash price $ 850 is available on the following terms: A deposit of $ 100 followed by equal payments at the end of each month for the next 18 months, if intere

Unit circle, Unit circle: The unit circle is one of the most valuable tool...

Unit circle: The unit circle is one of the most valuable tools to come out in trig.  Unluckily, most people don't study it as well. Below is the unit circle with just the first

1, 5 hockey pucks and three hockey sticks cost $23. 5 hockey pucks and 1 ho...

5 hockey pucks and three hockey sticks cost $23. 5 hockey pucks and 1 hockey stick cost $20. How much does 1 hockey puck cost?

Liner regression, Liner Regression The calculations for our sample siz...

Liner Regression The calculations for our sample size n = 10 are described below. The linear regression model is y = a + bx Table: Distance x miles

Number sequence, what is the formula to find a sequence on a string of numb...

what is the formula to find a sequence on a string of numbers?

Sets, creative assignment about sets

creative assignment about sets

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