1 + 1 + 1 + 1 + · · ·

1 + 1 + 1 + 1 + · · ·, also written $sum\_\{n=1\}^\{infin\}\; n^0$, is a divergent series.

Where it occurs in physical applications, 1 + 1 + 1 + 1 + · · · may sometimes be interpreted by zeta function regularization. It is the value at "s" = 0 of the Riemann zeta function:$zeta(s)=sum\_\{n=1\}^inftyfrac\{1\}\{n^s\},,$

in which the function is defined where the series diverges by analytic continuation. In this sense 1 + 1 + 1 + 1 + · · · = ζ(0) = −¹⁄₂.

Emilio Elizalde presents an anecdote on attitudes toward the series:

ee also

* Grandi's series

References