Partial sum of harmonic series as an improper fraction

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Discussion Overview

The discussion revolves around calculating a partial sum of the harmonic series expressed as an improper fraction. Participants explore methods for computing these sums, particularly for larger ranges, and discuss the capabilities of various calculators and software tools.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant shares their calculation of the partial sum from 1/2 to 1/10, resulting in the fraction 6,999,840/3,628,800, and expresses interest in finding a program for larger sums.
  • Another participant points out that the fraction can be simplified to 4861/2520 and questions whether the original calculator can perform sums.
  • A participant mentions using a Casio ClassPad to compute the sum up to 1/100, noting the complexity of the resulting expression.
  • A link to Wolfram Alpha is provided as a resource for calculating the sum of the harmonic series.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best method for calculating the sums or the capabilities of different calculators, indicating multiple competing views on the tools available for this task.

Contextual Notes

There are limitations regarding the simplification of fractions by calculators, and the discussion does not resolve the efficiency or accuracy of various methods for larger sums.

Who May Find This Useful

Individuals interested in harmonic series, mathematical computation, or those seeking tools for calculating sums in a mathematical context may find this discussion relevant.

starfish99
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I am interested in calculating a a partial sum of harmonic series as an improper fraction.

I added 1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10 with my calculator by finding a common denominator and got the fraction 6 999 840/3 628 800. It would take some time to do it for 1/2+1/3+...1/100.

Is there any program that can create these fractions for any partial harmonic sum?
 
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Your calculator didn't simplify. \frac{6999840}{3628800} simplifies to \frac{4861}{2520} .

As for doing it up to 100, does your calculator do sums? I have a casio classpad, which is similar in capabilities to a TI 89, and it does sums.

Woah, I just had it do up to 1/100, and it's loooooooong. If your calculator isn't going to simplify it, it's going to be crazy.

From what I hear a TI 83 will do it.
 
Last edited:
Thanks Gib Z
 

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