# Homework

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

thanks
• Apr 27th 2006, 06:38 AM
TD!
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 AM
miss_lolitta
Sorry i mean this sum:
$\displaystyle \sum-{i=1}^{\infty}1\frac{{i}^2}$??
• Apr 27th 2006, 06:46 AM
TD!
Still not there, do you mean

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

?
• Apr 27th 2006, 06:50 AM
miss_lolitta
yes thanks
• Apr 27th 2006, 06:52 AM
TD!
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 AM
miss_lolitta
thank u sooooooooooooooo much
• Apr 27th 2006, 07:05 AM
TD!
You're welcome :)