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 that the card is a 8 or an ace, A standard deck of cards conta...

A standard deck of cards contains 52 cards. One card is selected at random. Determine a)    The probability that the card is a 8 or an Ace? b)    The probability that the card is

Application of derivatives, the base b of a triangle increases at the rate ...

the base b of a triangle increases at the rate of 2cm per second, and height h decreases at the rate of 1/2 cm per second. Find rate of change of its area when the base and height

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

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

Accumulated amount , $26,000 is spended for two years. In the first year it...

$26,000 is spended for two years. In the first year it gets interest at 8.3% p.a. compounded semi annually. In the same year the rate of interest changes to 7.5% p.a. compounded da

Determine the numbers of sides in regular polygon, If each interior angle o...

If each interior angle of a regular polygon has a calculated as of 144 degrees, Determine the numbers of sides does it have? a. 8 b. 9 c. 10 d. 11   c. The measur

Matrix, find the matrix of the linear transformations T:R2->R2 defined by T...

find the matrix of the linear transformations T:R2->R2 defined by T(x,y,z)=(x+2y,x-3z).

Solve the limit problem, Solve the Limit problem as stated  Limit x tends...

Solve the Limit problem as stated  Limit x tends to 0 [tanx/x]^1/x^2 is ? lim m tends to infinity [cos (x/m)] ^m is? I need the procedure of solving these sums..

Determine the area of the matting, A circular print is being matted in a sq...

A circular print is being matted in a square frame. If the frame is 18 in by 18 in, and the radius of the print is 7 in, what is the area of the matting? (π = 3.14) a. 477.86 in

Example of cartesian coordinate graph, Example of Cartesian coordinate Grap...

Example of Cartesian coordinate Graph: Example:   The temperature of water flowing in a high pressure line was measured at regular intervals.  Plot the subsequent recorded da

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