Date: Oct 6, 2017 11:21 AM
Author: Karl-Olav Nyberg
Subject: Re: Can two series, both diverges, multiplied give a series that converges?
fredag 6. oktober 2017 17.13.31 UTC+2 skrev Peter Percival fĂ¸lgende:

> konyberg wrote:

> > 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,

>

> What is the definition of the product of two infinite series?

>

>

> > 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

> >

>

>

> --

> Do, as a concession to my poor wits, Lord Darlington, just explain

> to me what you really mean.

> I think I had better not, Duchess. Nowadays to be intelligible is

> to be found out. -- Oscar Wilde, Lady Windermere's Fan

It is the multiplication of the two series.

KON