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