Proving a Continuing Series: Methods

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Discussion Overview

The discussion revolves around methods to prove that the sum of the series Sum(1/x) from x=1 to n is never an integer. Participants explore examples and suggest approaches for proving this claim, focusing on mathematical reasoning and notation.

Discussion Character

  • Exploratory, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant suggests that the sum Sum(1/x) from x=1 to n is never an integer and provides an example with specific values (n=10) to illustrate this point.
  • Another participant emphasizes the importance of using LaTeX for clarity in mathematical expressions and provides a link to resources for learning LaTeX.
  • There is a suggestion to generalize the reasoning based on the factors of the numerator and denominator from the provided example.
  • A participant mentions the necessity of using PDF documents for attachments, indicating a preference for certain formats in the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a definitive proof method, and multiple approaches and suggestions are presented without resolving the question of whether the sum is never an integer.

Contextual Notes

Some assumptions regarding the properties of the series and integer values are not explicitly stated, and the discussion relies on specific examples without a general proof being established.

viren_t2005
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can u tell an appropriate method to prove this.
 

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it'll be a lot easier if you type it out here in plain text or latexed mark up.
 
The question as I see it is to show Sum(1/x), x=1 to n is never an integer. Well, take an example: Sum(1/x) x=1 to x=10 = 7381/2520. The factors of 7381 are 11^2x61, while the factors of 2520 are
2^3x3^2x5x7, so it can not be an integer.

From this example, you can proceed to find a general reason.
 
If you must attach a document please make it a PDF document. You can download Open Office here: http://www.openoffice.org/. It's free and it can open Microsoft Word Documents as well as being able to export to PDF. I also find its equation writer far more efficient and easy than Microsoft’s.

But even more usefully, just learn this boards LaTeX: https://www.physicsforums.com/showthread.php?t=8997

It allows you to quickly and easily write mathematical notation:

[tex]1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n}[/tex]

Prove this is never an integer [itex]\forall \, n > 1[/itex]

Anyway, robert has given sufficient help for you to start it.
 
Last edited:

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