# Thread: Geometric Series challenging question

1. ## 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.

2. ## Re: Geometric Series challenging question

So no one knows how to answer this?

3. ## Re: Geometric Series challenging question

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?

4. ## Re: Geometric Series challenging question

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

5. ## Re: Geometric Series challenging question

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 $\displaystyle (-1)^{1-1}=1~?$

If so, no wonder you are having trouble.

6. ## Re: Geometric Series challenging question

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

If so, no wonder you are having trouble.