Prove that the following infinite sum is convergesCauchy Criterion.using

(Headbang)

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- July 28th 2010, 05:53 PMAlso sprach ZarathustraCauchy Criterion.
Prove that the following infinite sum is converges

Cauchy Criterion.**using**

(Headbang) - July 29th 2010, 02:15 AMAckbeet
Just to clarify, you're trying to show that

converges, correct? And you're required to use the Cauchy criterion?

What have you done so far? - July 29th 2010, 02:47 AMAlso sprach Zarathustra
Yes.

I say the next thing:

So, I need to prove that for every , exist , for all , , and for all natural:

I choose .

My is not containing ... - July 29th 2010, 04:01 AMDinkydoe
How about this then...

Choose and write:

We need to show that for all we can find such that for all and we have

We can write:

since for all we may assume (with triangle inequality)

Now it can't be too hard to show that we can find such that for all and we have

**and**