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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.
Determine or find out if the following series converges or diverges. If it converges find out its value. Solution We first require the partial sums for this series.
I am learning this at school today and I started getting confused which one is which, can you help me?
If the areas of three adjacent faces of cuboid are x, y, z respectively, Find the volume of the cuboids. Ans: lb = x , bh = y, hl = z Volume of cuboid = lbh V 2 = l 2 b 2
Determine the area of the regular octagon with the following measurements. a. 224 square units b. 112 square units c. 84 square units d. 169 square units b. See
#subtraction of binary numbers methods
Tabulated values of the dynamic and kinematic viscosity of aqueous sodium chloride solutions have been researched in the academic literature (Kestin et al 1981). The data availab
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How do I solve this problem: Manuel is a cross-country runner for his school’s team. He jogged along the perimeter of a rectangular field at his school. The track is a rectangle th
methodology of OR
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