can someone find $\displaystyle \sum-{i=1}^{\infty}1\frac{i}$??

thanks

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- Apr 27th 2006, 06:31 AMmiss_lolittaHomework
can someone find $\displaystyle \sum-{i=1}^{\infty}1\frac{i}$??

thanks - Apr 27th 2006, 06:38 AMTD!
Your LaTeX-code isn't right but from the code I suspect you mean

$\displaystyle \sum\limits_{i = 1}^{ + \infty } {\frac{1}{i}} $

If so, this sum (harmonic series) diverges. - Apr 27th 2006, 06:41 AMmiss_lolitta
Sorry i mean this sum:

$\displaystyle \sum-{i=1}^{\infty}1\frac{{i}^2}$?? - Apr 27th 2006, 06:46 AMTD!
Still not there, do you mean

$\displaystyle

\sum\limits_{i = 1}^{ + \infty } {\frac{1}{i^2}}

$

? - Apr 27th 2006, 06:50 AMmiss_lolitta
yes thanks

- Apr 27th 2006, 06:52 AMTD!
That's a very well-known problem with the nice answer $\displaystyle \frac{\pi^2}{6}$ but it's not trivial to find this result.

This pdf file contains 14 (!) different proofs for it, some a bit more understandable than others, depending on your mathematical background. - Apr 27th 2006, 07:00 AMmiss_lolitta
thank u sooooooooooooooo much

- Apr 27th 2006, 07:05 AMTD!
You're welcome :)