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A harmonic sequence is a sequence of numbers in which the reciprocal of each term forms an arithmetic progression. In other words, the ratio between consecutive terms is constant when the reciprocals of the terms are taken. It is the equivalent of an arithmetic progression in terms of reciprocals.

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How do you generate harmonic progression?

If a sequence A = {a1, a2, a3, ... } is an arithmetic progression then the sequence H = {1/a1, 1/a2, 1/a3, ... } is a harmonic progression.


What is harmonic sequence?

It is a progression of terms whose reciprocals form an arithmetic progression.


What is a sequence that converges to 0 but the series diverges?

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It is a sequence of numbers. That is all. The sequence could be arithmetic, geometric, harmonic, exponential or be defined by a rule that does not fit into any of these categories. It could even be random.


Why is there no formula in getting the sum of a harmonic sequence?

A harmonic sequence is defined as a sequence of the form ( a_n = \frac{1}{n} ), where ( n ) is a positive integer. The sum of a harmonic series, ( \sum_{n=1}^{N} \frac{1}{n} ), diverges as ( N ) approaches infinity, meaning it grows without bound. Unlike arithmetic or geometric series, which have closed-form sums due to their consistent growth patterns, the harmonic series does not converge to a finite limit, making it impossible to express its sum with a simple formula. Thus, while there are approximations (like the use of logarithms), there is no exact formula for the sum of an infinite harmonic series.


Repetition of the same melodic pattern at different pitch levels?

That is called a sequence in music. It is a technique where a melodic or harmonic pattern is repeated at different pitch levels. This can create a sense of unity and development in the music.


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Harmonic elements in music refer to the combination of different notes played together to create chords and harmony, while melodic elements focus on the sequence of individual notes played one after the other to create a melody. In simpler terms, harmony is about how notes sound together, while melody is about how notes sound in a sequence.


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It is 3.562963 approx. a = 0.009009... recurring. d = 0.033957 approx


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