They say when s = 1...........the harmonic series increases w/o bound.........I don't think so....

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for any positive real number p. When p = 1, the p-series is the harmonic series, which diverges. Either the integral test or the Cauchy condensation test shows that the p-series converges for all p > 1 (in which case it is called the over-harmonic series) and diverges for all p ≤ 1.

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What is a harmonic in music?

A harmonic series is the sequence of sounds where the base frequency of each sound is an integral multiple of the lowest base frequency. Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously.

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Do harmonic series converge?

Why does the harmonic series diverge but the p-harmonic series converge. I am struggling understanding intuitively why the harmonic series diverges but the p-harmonic series converges. I know there are methods and applications to prove convergence, but I am only having trouble understanding intuitively why it is.

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Harmonic Series -- from Wolfram MathWorld

mathworld.wolfram.com › Calculus and Analysis › Series › General Series

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by EW Weisstein - ‎2004 - ‎Cited by 1 - ‎Related articles

converges to the natural logarithm of 2. An explicit formula for the partial sum of the alternating series is given by. (12) Gardner (1984) notes that this series never reaches an integer sum. The partial sums of the harmonic series are plotted in the left figure above, together with two related series.

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for any positive real number p. When p = 1, the p-series is the harmonic series, which diverges. Either the integral test or the Cauchy condensation test shows that the p-series converges for all p > 1 (in which case it is called the over-harmonic series) and diverges for all p ≤ 1.

‎Harmonic number · ‎Overtone · ‎Jeep problem · ‎List of sums of reciprocals

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