3
$\begingroup$

Possible Duplicate:
Why does $1+2+3+\dots = {-1\over 12}$?

Fermat's Dream by Kato et al. gives the following:

  1. $\zeta(s)=\sum\limits_{n=1}^{\infty}\frac{1}{n^s}$ (the standard Zeta function) provided the sum converges.

  2. $\zeta(0)=-1/2$

Thus, $1+1+1+...=-1/2$ ? How can this possibly be true? I guess I'm under the impression that $\sum 1$ diverges.

  • 0
    This (type of) question was also discussed here: http://math.stackexchange.com/questions/25014/erroneous-numerical-approximations-of-zeta-left-frac12-right/25019#250192011-09-21

1 Answers 1

2

As GEdgar noted, the zeta function is extended to values for which the series diverges via an analytic continuation.

  • 1
    Ok this helps, I guess I need to study analytic continuation.2011-09-21