firstname.lastname@example.org (S. Enterprize Company) wrote in <a href="news://email@example.com:">news://firstname.lastname@example.org:</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.
-- Timothy M. Brauch NSF Fellow Department of Mathematics University of Louisville