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Topic:
Can two series, both diverges, multiplied give a series that converges?
Replies:
22
Last Post:
Oct 7, 2017 12:52 AM
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Re: Can two series, both diverges, multiplied give a series that
converges?
Posted:
Oct 6, 2017 11:13 AM
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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
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