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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.
Fermat's Theorem : If f ( x ) contain a relative extrema at x = c & f ′ (c ) exists then x = c is a critical point of f ( x ) . Actually, it will be a critical point such that f
The sum of the smallest and largest multiples of 8 up to 60 is?
find k,is -2 a root of the equation 3x2
1. Consider the code of size 4 (4 codewords) and of length 10 with codewords listed below. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1
Give an examples of Simplifying Fractions ? When a fraction cannot be reduced any further, the fraction is in its simplest form. To reduce a fraction to its simplest form,
What is Deductive Reasoning ? Geometry is based on a deductive structure -- a system of thought in which conclusions are justified by means of previously assumed or proved sta
Complementary addition -what number how many things should be added to one number or group to get the other. (e.g., a classroom can seat 50 children, and 20 children are already s
Newton's Second Law of motion, which recall from the earlier section that can be written as: m(dv/dt) = F (t,v) Here F(t,v) is the sum of forces which act on the object and m
Define the Probability Transition Matrices or Brand switching.
1+2i=a+ib so find a and b
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