{Sn} does NOT converge, because since a1, b1, and c1 are all bigger than one, and because they're bigger than one, this logically implies that they are all positive.

Because they are all positive, the 1/2^2548(variable + variable) part in each series will never dip below zero (i.e. become negative), and so the value will be forever increasing. Granted, it will be increasing at infinitely smaller intervals, but it will still be increasing. Thus, the series cannot converge.

Closest thing I can figure for this being related to poker is that this has to do with teh Fourier Transformation, which has to do with sinusoidal curves. The sinusoidal curves then would represent variance in poker. Because the series' don't converge, that would mean not all poker players will get to the same point in the long run (i.e. lose their money to each other to the point where everyone is exactly equal). The long run is infinity here, obviously.

Then, the series would prove that good poker players are able to deviate from losing their money to everyone in general by taking money from bad players. And because the series are continually going upwards, that as time went on (and presumably, good players moved up in limits), variance would get smaller and smaller.

That's the best I can do as far as a reference to poker. You'd better have something godo for making me solve those stupid series. Took me like half an hour.