Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: .99999... still=/= 1
Replies: 43   Last Post: Dec 8, 2004 3:31 PM

 Messages: [ Previous | Next ]
 Tim Brauch Posts: 201 Registered: 12/6/04
Re: .99999... still=/= 1
Posted: Dec 2, 2004 11:24 PM

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>

&gt;
&gt; A Harmonic Series is an exception to the rule. The above shown
&gt; series
&gt; appears to be a harmonic series similar to,
&gt;
&gt; 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