Harmonic progression (h.p.), Mathematics

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.

Posted Date: 9/13/2012 4:43:42 AM | Location : United States







Related Discussions:- Harmonic progression (h.p.), Assignment Help, Ask Question on Harmonic progression (h.p.), Get Answer, Expert's Help, Harmonic progression (h.p.) Discussions

Write discussion on Harmonic progression (h.p.)
Your posts are moderated
Related Questions
Julie had $500. She spent 20% of it on clothes and then 25% of the remaining money on CDs. How much money did Julie spend? Find out 20% of $500 by multiplying $500 by the decim

Graph y = sin ( x ) Solution : As along the first problem in this section there actually isn't a lot to do other than graph it.  Following is the graph. From this grap

how i do project in linear programming in agriculture

The 5% sales tax on a basket was $0.70. What was the price of the basket? Use a proportion to solve the problem; part/whole = %/100. The whole is the price of the basket (wh

Q. Graphs of Sin x and Cos x ? Ans. The sine and cosine functions are related to the path that an object might take around a circle. Suppose a dolphin was swimming over

is 1/6 same as six times less

calculates the value of the following limit. Solution Now, notice that if we plug in θ =0 which we will get division by zero & so the function doesn't present at this

similarities between rectangle & parallelogram

#The digits 1,2,3,4and 5 are arranged in random order,to form a five-digit number. Find the probability that the number is a. an odd number. b.less than 23,000