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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.
Inflation The inflation rate for a given period can be calculated using the following formula; Inflation = (current retail price index/retail price index in the base year)
as part of the markwting mix
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maximize Z=2x+5y+7z, subject to constraints : 3x+2y+4z =0
Evolve a game to help children remember basic multiplication facts. In this section we have looked at ways of helping children absorb some simple multiplication facts. But what
OTHER WAYS TO AID LEARNING : Here we shall pay particular attention to the need for repetition, learning from other children, and utilising errors for learning.
howmany numbers made by digit 0,1,2,3,5,7,9 but any digit isnot repeted
Explain Adding Rational Expressions with Different Denominators When you add or subtract fractions or rational expressions that have different denominators, you must first find
the cost of paint used in a redecorating job is $65.70 .This is a reduction from its original cost of $82.13 .What is the percent decrease in the cost of paint to the nearest perce
Prove that if f and g are functions, then f intersect g is a function by showing f intersect g = glA A={x:g(x)=f(x)}
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