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What are Harmonic Sequences?
in Mathematics by Diamond (61,678 points) | 4 views

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A series of numbers is said to be in harmonic sequence if the reciprocals of all the terms of the sequence form an arithmetic sequence.

*Remember the reciprocal of $a$ is $\dfrac{1}{a}$ meaning the reciprocal of $\dfrac{1}{3}$ is $3$. To test whether two numbers are reciprocals of each other, simply multiply them and if the answer is $1$ then it implies they pass the reciprocal test.

For example:

The sequence

\[\dfrac{1}{4};\dfrac{1}{6};\dfrac{1}{8};\dfrac{1}{10};\dfrac{1}{12};...\]

So what we have to do is to prove that the reciprocals of the terms in the sequence form an arithmetic sequence.

The reciprocals are as follows:

\[4;6;8;10;12;...\]

*Whenever you are given Harmonic Progression convert it into A.P

 

 

by Diamond (61,678 points)

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