This is the series:

So this is what I did:

So the first term diverges because it is harmonic and thus the hole series diverges.

I have this marked as wrong, but I don't understand why. Can somebody explain it please?

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- Jul 20th 2008, 02:12 PMasciiAnalize convergence of an infinite series
This is the series:

So this is what I did:

So the first term diverges because it is harmonic and thus the hole series diverges.

I have this marked as wrong, but I don't understand why. Can somebody explain it please? - Jul 20th 2008, 02:13 PMMathstud28
- Jul 20th 2008, 02:18 PMascii
Oh thank you... so if there was a plus between the series they would diverge for sure.

I'll try other way.

Thanks again - Jul 20th 2008, 02:19 PMarbolisQuote:

So the first term converges because it is harmonic

- Jul 20th 2008, 02:26 PMascii
- Jul 20th 2008, 02:39 PMascii
Ok so I got this series:

Which converges as the limit comparison with 1/n^2 confirms.

But now I'm asked to express the result of the sum.

I think this is a telescoping series, isn't it?

If it is, then the sum is equal to the limit when N goes to infinity of the first term minus the N-th term? - Jul 20th 2008, 02:42 PMThePerfectHacker
- Jul 20th 2008, 02:44 PMascii
So if I want to know the sum of a telescoping I have to express a few terms and see how they cancel?

- Jul 20th 2008, 03:00 PMPlato
The series is very nice example of a

*collapsing sum*.

A partial sum of the series looks this:

Now it simple to see that ,

Therefore the series converges, - Jul 20th 2008, 03:07 PMascii
- Jul 20th 2008, 03:22 PMPlato
- Jul 20th 2008, 03:25 PMascii
Thank you.

- Jul 21st 2008, 12:24 AMMoo
Hello,

Be very careful !

The sum of a divergent series and a convergent series is indeed**divergent**.

But the sum of 2 divergent series is not**necessarily divergent**.

------------------

Another way of doing it :

We can transform the second one by changing the indice :

So the sum is now :

- Jul 21st 2008, 12:32 AMkalagota
- Jul 21st 2008, 12:37 AMMoo