This was a problem in my test this morning. I was not able to answer it. :( But I thought it was pretty interesting, and would like to know the answer. Could you guys help me out? :)

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- Nov 10th 2010, 02:04 AMmetallicsatanInfinite Series and Limits
This was a problem in my test this morning. I was not able to answer it. :( But I thought it was pretty interesting, and would like to know the answer. Could you guys help me out? :)

- Nov 10th 2010, 02:32 AMtonio
- Nov 10th 2010, 03:18 AMAlso sprach Zarathustra
.

- Nov 10th 2010, 07:04 AMmetallicsatan
- Nov 10th 2010, 08:43 AMtonio
- Nov 10th 2010, 09:57 AMmetallicsatan
I can only think of but the problem is, the summation does not have a partition, if that is the case. Any more hints?

- Nov 10th 2010, 10:11 AMtonio
- Nov 10th 2010, 10:55 AMmetallicsatan
so is ? and . If that is the case, the limit is equal to ? Right? I'm not sure. (Thinking)

- Nov 10th 2010, 11:07 AMHallsofIvy
This is incorrect. Dividing both numerator and denominator of by gives . And, now, unfortunately, that is NOT the same as [/tex]\frac{1}{1+ x^2}[/tex].

Perhaps dividing both numerator and denominator by giving so we can think of it as a Riemann sum for will work.

Quote:

To what familiar and very easy to integrate function's Riemann sum does the last sum above ressemble?(Nerd)

And in what interval, of course?

Tonio

- Nov 10th 2010, 11:13 AMmetallicsatan
Now I have totally no idea what to do. Any more hints?

- Nov 10th 2010, 12:35 PMAlso sprach Zarathustra
In my poor opinion this problem can be solved without using Riemann sums... ( Thinking in a new direction)

- Nov 10th 2010, 12:58 PMmetallicsatan
- Nov 10th 2010, 01:00 PMmetallicsatan
- Nov 10th 2010, 07:28 PMtonio
- Nov 10th 2010, 11:56 PMineedyourhelp