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[tex] \sum_{n=-\infty}^{\infty} f(n) [/tex]

which I do not want to consider the convergence of in the normal sense, but I want to talk about the limit

[tex] \lim_{N\to \infty} \sum_{n=-N}^{N} f(n). [/tex]

I know that when this limit exists the sum is _____ convergent, or is a _____ sum, where _____ is something like principal, or first order, or perhaps a name like a Dirichlet sum (I'm making these up of course). Does anybody know what the word I am looking for is?