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Three quantities a, b and c are said to be in harmonic progression if,
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
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
This can be written as
Canceling the common terms, we have
This gives us the common difference between the reciprocal terms of a, b and c. This also proves our proposition.
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2-3+=3+-4
how to get the answer
what is a perfect square
Area with Parametric Equations In this section we will find out a formula for ascertaining the area under a parametric curve specified by the parametric equations, x = f (t)
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Can anybody suggest me any example of Set Representation?
Before we look at this, let us learn what a multiple is. Take any number say 3. Multiply this number with natural numbers. We obtain 3, 6, 9, 12, 15, 18,.........
integrate sin(x) dx
Question 1. Use cylindrical coordinates to nd the mass of the solid of density e z which lies in the closed region Question 2. The density of a hemisphere of radius a (y
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