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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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 bursejan@gmail.com Posts: 5,511 Registered: 9/25/16
Re: Can two series, both diverges, multiplied give a series that converges?
Posted: Oct 6, 2017 12:48 PM

Depends, try it with the definition here:

MATH 304: CONSTRUCTING THE REAL NUMBERS,
Peter Kahn Spring 2007
http://www.math.cornell.edu/~kahn/reals07.pdf

See page 12, 4.2 Algebraic operations on sequences

The lecture above expounds that when the first series
{sn} converges (by Cauchy criteria) and the second
series {tn} converges (by Cauchy criteria) , then the

result {sn}*{tn} will also converge (by Cauchy criteria).
If one of the series diverges then this theorem of
the lecture above is no use for you.

I would say everything is possible, like:

oo * 0 = 0

oo * 0 = oo

oo * 0 = c

oo * 0 = undefined

Am Freitag, 6. Oktober 2017 18:24:33 UTC+2 schrieb konyberg:
> One a goes to inf, the other goes to 0. What is now the product?
> You can not tell if you do not know the functions defining the entities.
> KON