Marc writers: << This summer's AMS Notices reproduces Ramanujan's letter to Hardy where he asserts 1 + 2 + 3 + 4 + ... = - 1/12 On the hypothesis that even the errors of genius may hold value, I've always been curious what his theory was under which this result was derived.

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I've seen it written in several places that since 1+2+3+ . . . = sum{n=1,oo} of 1/n^(-1), Ramanujan thought of this sum, in some sense, as zeta(-1), which turns out (using correct analytic continuation of the Dirichlet series zeta(s) = sum{n=1,oo} of 1/n^s, which converges only for Re(s) > 1) to be -1/12. --Dan