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Re: .99999... still=/= 1
Posted:
Dec 2, 2004 11:24 PM
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smart1234@aol.com (S. Enterprize Company) wrote in
<a href="news://20041202054510.06111.00000837@mb-m23.aol.com:">news://20041202054510.06111.00000837@mb-m23.aol.com:</a>
>
> A Harmonic Series is an exception to the rule. The above shown
> series
> appears to be a harmonic series similar to,
>
> 1 + 1/2 + 1/3 + 1/4 + ....
Yes, this is harmonic and diverges. However, the series
1 + 1/2 + 1/4 + 1/8 + 1/16 + ...
is not harmonic and converges. It is geometric with r = 1/2. Look in your
books for a geometric series and find out when it converges and when it
diverges.
Just because something (1 + 1/2 + 1/4 + 1/8 + ...) might somehow resemble
something else (1 + 1/2 + 1/3 + 1/4 + ...), does not at all mean they are
similar in any way. Surely an apple and a wax apple look similar.
However, I would rather bite into the former than the latter.
- Tim
--
Timothy M. Brauch
NSF Fellow
Department of Mathematics
University of Louisville
email is:
news (dot) post (at) tbrauch (dot) com
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