Thread: Srinivasa Ramanujan proved that 1+2+3+... = -1/12???

Went to see dissapearing number last night at the Barbican. Apparently,

Srinivasa Ramanujan proved that 1+2+3+... = -1/12, I believe using the zet function?

Can anyone explain how this can be. I am high sch maths teacher, but would like to see how this is proved.
If you can help, I would really appreciate it.

Thanks

Mrt1

Originally Posted by mrt1

Went to see dissapearing number last night at the Barbican. Apparently,

Srinivasa Ramanujan proved that 1+2+3+... = -1/12, I believe using the zet function?

Can anyone explain how this can be. I am high sch maths teacher, but would like to see how this is proved.
If you can help, I would really appreciate it.

Thanks

Mrt1

Google for "Ramanujan summation"

CB

I need some help with this. Every wb page I look at is either full of maths, I've not seen for years, or these is a proof in a physics forum that

Ramanujan Summation and Divergent series in relation to the Riemann Zeta function. I'm not sure is concrete.

What is the R next to the -1/12?

Mark

Originally Posted by mrt1

I need some help with this. Every wb page I look at is either full of maths, I've not seen for years, or these is a proof in a physics forum that

Ramanujan Summation and Divergent series in relation to the Riemann Zeta function. I'm not sure is concrete.

What is the R next to the -1/12?

Mark

It denote that the summation in question is not a normal summation (which is just as well since the series are in any conventional sense are divergent), but is a Ramanujan sum, which is a rather different beast.

CB