1 + 2 + 3 + 4 + 5.... = -1/12?

[JohnClay]

ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12

Sum of Natural Numbers (second proof and extra footage)

Thanks for the messages

Ramanujan summation

Using standard extensions for known divergent series, he calculated “Ramanujan summation” of those. In particular, the sum of 1 + 2 + 3 + 4 + ⋯ is -1/12 where “R” indicates Ramanujan summation.

…the Ramanujan summation of a divergent series is not a sum in the traditional sense, it has properties which make it mathematically useful in the study of divergent infinite series, for which conventional summation is undefined…

The Numberphile videos imply that 1 + 2 + 3… = -1/12 but it seems that they’re not talking about the traditional sum.

They said something about it being useful in physics and I think string theory…

I think the sum is infinite or at least a non-negative number. I wonder why it is -1/12? I mean why not pi or something…
More:

1 + 2 + 3 + 4 + ⋯

[Indistinguishable]

See the other current thread (and the older thread).

[Colibri]

Since there is an active thread on this, I’m closing this one.

Colibri
General Questions Moderator