1. 1+2+3+...=-1/12

Hi, could you explain precisely why
$\displaystyle 1+2+3+...=-\frac{1}{12}$

I know it involves applying one of the functional equations of the Riemann Zeta function, but as I'm not too familiar with the zeta function, could you explain in a bit more depth? Our lecturer just rushed through it...

Thanks a lot

2. Srinivasa Iyengar Ramanujan was an Indian mathematician 'self taught genius' ... and because I am a 'common mortal' is likely I don't undestand most of his 'mathematical discoveries' ...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

3. Originally Posted by tunaaa
Hi, could you explain precisely why
$\displaystyle 1+2+3+...=-\frac{1}{12}$

I know it involves applying one of the functional equations of the Riemann Zeta function, but as I'm not too familiar with the zeta function, could you explain in a bit more depth? Our lecturer just rushed through it...

Thanks a lot

Read here: Wapedia - Wiki: Ramanujan summation , and please do pay attention in which sense the above sum is true.

Tonio