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Class 10 > Learn Class IX-X Tuition > What is harmonic progression?
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What is harmonic progression?

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It is a progression formed by taking the reciprocals of an arithmatic progression.1/a,1/a+d,1/a+2d,1/a+3d,.........1/a+kd. the harmonis term means neighboring terams.
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"Read , Recall and Procure"

The reciprocal of arithmetic progression is harmonic progression.
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The simplest way to define a harmonic progression is that if the inverse of a sequence follows the rule of an arithmetic progression then it is said to be in harmonic progression. This simply means that if a, a+d, a+2d, ….. is an A.P. then 1/a, 1/(a+d), 1/(a+2d), …… is an H.P. For example, the series...
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The simplest way to define a harmonic progression is that if the inverse of a sequence follows the rule of an arithmetic progression then it is said to be in harmonic progression. This simply means that if a, a+d, a+2d, ….. is an A.P. then 1/a, 1/(a+d), 1/(a+2d), …… is an H.P. For example, the series 1 +1/4 +1/7 +1/10 +..... is an example of harmonic progression, since the series obtained by taking reciprocals of its corresponding terms i.e. 1 +4 +7 +10 +... is an A.P. read less
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A series of non-zero numbers is said to be harmonic progression (abbreviated H.P.) if the series obtained by taking reciprocals of the corresponding terms of the given series is an arithmetic progression. For example, the series 1 +1/4 +1/7 +1/10 +..... is an H.P. since the series obtained by taking...
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A series of non-zero numbers is said to be harmonic progression (abbreviated H.P.) if the series obtained by taking reciprocals of the corresponding terms of the given series is an arithmetic progression. For example, the series 1 +1/4 +1/7 +1/10 +..... is an H.P. since the series obtained by taking reciprocals of its corresponding terms i.e. 1 +4 +7 +10 +... is an A.P. read less
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Online Math Tutor for IGCSE & IB Boards with 20 years of teaching experience

If a sequence of numbers e.g. a,b,c,d.... be in Arithmetic Progression, then their reciprocals i.e. 1/a,1/b,1/c,1/d are said to be in Harmonic progression. The converse is also true which means that if numbers a,b,c,d be in Harmonic Progression then the numbers 1/a,1/b,1/c,1/d will follow the Arithmetic...
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If a sequence of numbers e.g. a,b,c,d.... be in Arithmetic Progression, then their reciprocals i.e. 1/a,1/b,1/c,1/d are said to be in Harmonic progression. The converse is also true which means that if numbers a,b,c,d be in Harmonic Progression then the numbers 1/a,1/b,1/c,1/d will follow the Arithmetic Progression rules. The sums of H.P. are usually solved by taking the reciprocals of the numbers, so that the rules of A.P. can be applied to them. read less
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In mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression. In other words, it is a sequence of the form 1/a ,1 \a+d , 1 \a+2d , 1 \a+3d , ... 1 \a+kd
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The reciprocal of arithmetic progression is harmonic progression.
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A sequence of quantities whose reciprocals are in arithmetical progression (e.g. 1, 1/3, 1/5, 1/7, etc.).
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Harmonic Progression(HP) is closely related to Arithmetic Progression(AP). On taking inverse of the given sequence, if we find that it comes out to be an AP then the given sequence is a HP.
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