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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.
limit x APProaches infinity (1+1/x)x=e
what is the muttiplied number of mutttiplacation called
5to6
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2/3 - 7/12
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an insurance salesman sells policies to 5 men, all of identical age in good health. the probability that a man of this particular age will be alive 30 years hence is 2/3.Find the p
how do you solve simultaneous equation?
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