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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.
Variance Consider the example of investment opportunities. The expected gains were Rs.114 and Rs.81 respectively. The fact is that an investor also looks at the dispersion befo
Method In this method we eliminate either x or y, get the value of other variable and then substitute that value in either of the original equations to
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The perimeter of Andrew''s rectangular room is 44 feet. What equation was used to find the perimeter?
Q. How to Convert Decimals to Percentages? Ans. Remember that when you have a decimal number, the digits to the right of the decimal point have the following meaning:
X-intercept If an intercept crosses the x-axis we will call it as x-intercept . Y-intercept Similar, if an intercept crosses the y-axis we will call it as a y-inter
how to divide a binaries
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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
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