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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: subseries of harmonic series converges iff ...
Replies: 5   Last Post: Nov 21, 2004 9:11 AM

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Michael Hamm

Posts: 14
Registered: 12/10/04
subseries of harmonic series converges iff ...
Posted: Nov 18, 2004 4:14 PM
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I recall reading a theorem once that says
For a subset S of Z+ , the following are equivalent:
* \Sum_{s \in S} 1/s < \infty
* Something else.

Does anyone know what that something else is? If this helps, I seem to
recall that the something-else was sufficiently complicated that one would
never use it to prove a series convergent or divergent: the implication
would go the other way.

Michael Hamm
AM, Math, Wash. U. St. Louis
msh210@math.wustl.edu Standard disclaimers:
<a href="http://math.wustl.edu/~msh210/">http://math.wustl.edu/~msh210/</a> ... legal.html

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