Harmonic series and 𝑝-series | AP®︎ Calculus BC | Khan Academy



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𝑝-series is a family of series where the terms are of the form 1/(nᵖ) for some value of 𝑝. The Harmonic series is the special case where 𝑝=1. These series are very interesting and useful.

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13 Comments

  1. The harmonic series behaves differently when you graph the individual points versus the sum of those points. Individually the points start at one and decrease to zero. Their sum, however, starts at one and increases to about 4.5, but does not converge to one number, I have calculated it to 1/100, have round-off errors from working with 15 digit numbers. Its rate of increase slows, but never stops. I had my suspicions and found where they used a computer to evaluate it. The harmonic series does not approach a single number, it diverges

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