Geometric Series challenging question

• Jan 9th 2013, 11:47 PM
spriterman
Geometric Series challenging question
Suppose r and s are positive integers with no common factor and

1 - 1/2 + 1/3 - 1/4 + ... + 1/1339 - 1/1340 = r/s

Find a prime factor of r.

Please explain it step by step clearly. Thanks.
• Jan 10th 2013, 04:35 PM
spriterman
Re: Geometric Series challenging question
So no one knows how to answer this?
• Jan 10th 2013, 04:53 PM
Plato
Re: Geometric Series challenging question
Quote:

Originally Posted by spriterman
So no one knows how to answer this?

Oh no, many of us know what needs to be done.
But why do you think we should do your work for you?

Here it is.

Now what can you do with that?
• Jan 10th 2013, 05:09 PM
spriterman
Re: Geometric Series challenging question
Doesn't that equation make the 1 negative? The starting term of the series is a positive.
• Jan 10th 2013, 06:20 PM
Plato
Re: Geometric Series challenging question
Quote:

Originally Posted by spriterman
Doesn't that equation make the 1 negative? The starting term of the series is a positive.

Are you saying that you do not know that $(-1)^{1-1}=1~?$

If so, no wonder you are having trouble.
• Jan 11th 2013, 04:25 PM
spriterman
Re: Geometric Series challenging question
Quote:

Originally Posted by Plato
Are you saying that you do not know that $(-1)^{1-1}=1~?$

If so, no wonder you are having trouble.