[ilyagr]

To expound on Retric's comment (I expounded much more in a cousin thread): I also first assumed that what you said must be true. When I tried to check with a calculation, it turned out that the opposite is the case.

[darkmighty]

Yea, my bad. I implicitly made the rookie mistake of assuming that f(x)->0 implies sum(f(x))->0, as shown by Retric :)