Date: Oct 6, 2017 11:13 AM
Author: Peter Percival
Subject: Re: Can two series, both diverges, multiplied give a series that<br> converges?
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

>

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