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Originally Posted by OldDan1168
The sum of an infinite geometric series is A / (1 - R) where A is the First element of the series and R is the common ratio.
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note - only for R < 1.
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Originally Posted by OldDan1168
Meanwhile, this is a fascinating discussion, and I enjoyed reading everyone's thoughts. Someone mentioned the idea of 0/0. There's a name for it, and I seem to forget exactly what the name is (the name does make sense once you hear it). Anyway it's not 0; 0/0 is equal to INF/INF or 1^INF or 0^0 or any other myriad devilish expressions : it simply does not exist. I think it might be called an infinite discontinuity but that's just a guess.
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One of the best known applications of this is L'Hopital's rule, which is used for finding the integrals of certain functions that can be transformed into something that resembles one of those patterns - 0/0, inf/inf, inf-inf, 1^inf, 0^0, et cetera.