Date: Oct 6, 2017 11:02 AM
Author: Karl-Olav Nyberg
Subject: Re: Can two series, both diverges, multiplied give a series that converges?
fredag 6. oktober 2017 16.10.39 UTC+2 skrev Markus Klyver fĂ¸lgende:

> Den fredag 6 oktober 2017 kl. 15:42:22 UTC+2 skrev konyberg:

> > Consider these two series.

> > s = lim (n=1 to inf) Sum(1/n) and t = lim (n=1 to inf) Sum(1/(1+n)).

> > Both series diverges, going to infinity.

> > Now if we multiply these, we can argue that every product of the new series is smaller or equal to 1/n^2. So it should converge. Or can we?

> > Let us write the first as a series without the sigma and the other with sigma.

> > s*t = (1+1/2+1/3+ ...) * t. And since the first from s (1 * t) diverges, how can s*t converge?

> >

> > KON

>

> I'm not sure if the product will converge absolutely, but if multiplication is done in the naive way it'll converge.

So: limit * something = something (or limit)

Which is it?

Try it with (-1)^n and see if it is absolutely.

KON