Proving a Continuing Series: Methods

[viren_t2005]

can u tell an appropriate method to prove this.

 

[matt grime]

it'll be a lot easier if you type it out here in plain text or latexed mark up.

 

[robert Ihnot]

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.

 

[Zurtex]

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:

1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n}

Prove this is never an integer \forall \, n > 1

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