Re: harmonic series = convergant

From: Laserman (jimzotos_at_yahoo.com)
Date: 08/12/04 

Date: 11 Aug 2004 19:34:19 -0700

dwb1729@yahoo.com (David Bandel) wrote in message news:<a88af92f.0408071906.7cffbda0@posting.google.com>...
> dwb1729@yahoo.com (David Bandel) wrote in message news:<a88af92f.0408060923.5594f34f@posting.google.com>...
> > the proof that the harmonic series diverges is flawed. since the
> > subsequent terms get successively smaller, the series is clearly
> > approaching some finite value. what mathematicians fail to notice is
> > that just rewriting the series as a different series and showing that
> > THAT one diverges.. is not sufficient.
> >
> > they like to rewrite it this way:
> >
> > 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + ...
> >
> > 1/2 + 1/2 + 1/4 + 1/4 + 1/8 + 1/8 + 1/8 + 1/8 + 1/16... etc.
> >
> > showing the second diverges isn't enough.. all that shows is that
> > second series has diverged.
> >
> > the harmonic series clearly converges to some well-established value
> > that by now must have been easily realizeable by any mathematician..
> > but instead they conspire to keep it on the "down-low" so as to not
> > look like utter idiots.
> >
> > if a series is positive and decreasing.. the sum is finite.. that's
> > clear enough.
> > as the series reaches infinite term.. it's term will equal 0.. and u
> > will not be adding more. so the limit of this sum as it reaches it's
> > infinity term is clearly a finite value.
> >
> > now i am sure the majority of sci.math will try to refute this with
> > bogus logic.. but the truth is right in front of your eyes.
>
> that wasn't as fun as i thought it would be.

Seriously though, by showing that the second series has a smaller sum
than the first AND that the second series has an infinite sum
automatically guarantees that the first series has an infinite sum
because its sum is clearly bigger than the first. What you are saying
is that the harmonic series is bigger than infinity AND finite at the
same time. Clearly a paradoxical state of affairs.

Good night
Laserman

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