analysis - Why does $1+2+3+cdots = -frac{1}{12}$?

Thursday, September 17, 2015

analysis - Why does $1+2+3+cdots = -frac{1}{12}$ ?

$\displaystyle\sum_{n=1}^\infty \frac{1}{n^s}$ only converges to $\zeta(s)$ if $\text{Re}(s) > 1$ .

Why should analytically continuing to $\zeta(-1)$ give the right answer?

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