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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.
how do you regroup?
The base of an isosceles triangle and the altitude drawn from one of the congruent sides are equal to 18cm and 15cm, respectively. Find the lengths of the sides of the triangle.
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Solve the following equestions i.2x-8=8 ii.3x+2/5=4 iii.8/3x-2=2 iv.0.6x-5=7
a man in rested rupee 800 is buying rupee 5 shares and then are selling at premium of rupee 1.15. He sells all the shares.find profit
Logarithmic form and exponential form ; We'll begin with b = 0 , b ≠ 1. Then we have y= log b x is equivalent to x= b y The first one is called
What is Dividing Fractions? If you want to divide two fractions, you invert the second fraction (that is, turn it upside-down) and change the division sign to a multiplication
Pai is rational or irrational
A train covered a certain distance at a uniform speed. If the train would have been 6km/hr faster, it would have taken 4hours less than the scheduled time. And if the train were
tan^2=(secx-1)(secx+1)
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