From: utzoo!decvax!harpo!eagle!wb2!houxz!ihnp4!ihlpb!dap1 Newsgroups: net.math Title: Re: 1=/= .999... - (nf) Article-I.D.: ihlpb.285 Posted: Sat Jan 29 18:01:24 1983 Received: Mon Jan 31 04:20:58 1983 #R:rocheste:-52200:ihlpb:6200009: 0:778 ihlpb!dap1 Jan 29 16:42:00 1983 Whoooaaa! I hate to argue, but your S series most definitely does NOT converge to 1/4! You are thinking of Abel summability which is not the classical definition of convergence. The classical definition requires you to supply me a number N such that after N terms your series does not stray from 1/4 by more than an arbitrary epsilon. For epsilon < 1/4 you obviously cannot do this. Your series is Abel summable to 1/4. This result is gotten by representing your sum as a power series, summing the power series to obtain a formula and then using that formula outside the radius of convergence. This has it's uses, but doesn't represent classical convergence. For more info, see "Methods of Real Analysis" by Richard R. Goldberg, page 271. Darrell Plank BTL-IH