magfrump seems to have nailed it. I find it interesting how controversial that one has been :)

For infinite sums, basically, if the sum is infinite, then any finite probability gives it infinite expected utility (infinity * [1/N] = infinity). If both the sum and probability are finite, then one can argue the details (N * [1/N^2] < 1). The math is different between an arbitrarily large finite and an infinite. Or, at least, I've always assumed Pascal's Wager relied on that, because otherwise I don't see how it produces an infinite expected utility regardless of scepticism.