I need some help determining whether or not the equation in the attachment diverges or converges. I'm trying to teach myself the integral test, and cannot seem to get this one to work. Any help would be much appreciated.

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- July 18th 2008, 10:18 PMrman144Converges or Diverges?
I need some help determining whether or not the equation in the attachment diverges or converges. I'm trying to teach myself the integral test, and cannot seem to get this one to work. Any help would be much appreciated.

- July 18th 2008, 10:24 PMMathstud28
- July 18th 2008, 10:28 PMrman144Reply
No, I'm saying that "x" can be any value greater than one and less than positive infinity

- July 18th 2008, 10:31 PMMathstud28
- July 18th 2008, 10:33 PMrman144Reply
Sorry, I'm kind of new to this stuff. Yeah, you are correct. Still, how can I prove it diverges/converges?

- July 18th 2008, 10:58 PMMathstud28
Lets look at the integral

Now we can see that the first and last terms are

and respectively.

Now let us consider

If we use integration by parts once we get

Now if we let

and

So this would gives us

Now by letting and respectively we come up with

Now making the appropriate backsubs we get

Putting this all back together we get

So putting this completely back together and remembering that we get

(Whew)

Can you go from there? - July 18th 2008, 11:03 PMrman144Reply
Yeah, thanks a lot. This site saves lives

- July 18th 2008, 11:06 PMMathstud28
- July 18th 2008, 11:14 PMrman144Reply
Thanks, already done.

- July 19th 2008, 01:08 AMrman144Reply
I know that this is beating a dead horse, but I seem to still have a problem. The integral test keeps telling me the series converges, but the graph of the equation is basically telling me that it diverges. Am I just messing myself up on this one, or did I make a mistake with the integral test?

- July 19th 2008, 01:10 AMMathstud28