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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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Power rule: d(x n )/dx = nx n-1 There are really three proofs which we can provide here and we are going to suffer all three here therefore you can notice all of them. T
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#question.find the number of combinations of the letters a, b, c, and d taken 3 at a time.
Q. What are Inclusive Events? Ans. Events that can occur at the same time are called inclusive events. For example, a student can belong to more than one club at one time
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