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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.
need answer to integers that equal 36
1/8 of the passengers of a train were children.If there were 40 children travelling in the train on a certain day,how many adults were there in that train that day?
Product Rule: (f g)′ = f ′ g + f g′ As with above the Power Rule, so the Product Rule can be proved either through using the definition of the derivative or this can be proved
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Need assignment help, Explain Multiplication of two Matrices.
We want to find the integral of a function at an arbitrary location x from the origin. Thus, where I(x=0) is the value of the integral for all times less than 0. (Essenti
The sum of the smallest and largest multiples of 8 up to 60 is?
(x+y+1)dy/dx=1
how to solve this? y = 7x - 12 y = x2 Solve the system using substitution.
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