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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.
ion..
Q. Define Period, Amplitude and Phase Shift? Ans. Period, amplitude and phase shift are used when describing a sinusoidal curve The period of a function is the smallest
how to divide
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Randi takes the stairs at work whenever possible instead of the elevator. She must climb up 51 steps from her office to get to the accounting department. The human resources depa
1. Show that there do not exist integers x and y for which 110x + 315y = 12. 2. If a and b are odd integers, prove that a 2 +b 2 is divisible by 2 but is NOT divisible by 4. H
1+2i=a+ib so find a and b
2/2
Temperature: On one day in Fairfield, Montana the temperature dropped 80 degree fahrenheit from noon to midnight. If the temperature at midnight was -21 degree fahrenheit, write an
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