The Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
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
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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




Date Subject Author
10/6/17
Read Can two series, both diverges, multiplied give a series that converges?
Karl-Olav Nyberg
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that converges?
Markus Klyver
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that converges?
Karl-Olav Nyberg
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that converges?
Karl-Olav Nyberg
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that
converges?
Peter Percival
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that converges?
Karl-Olav Nyberg
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that
converges?
Mike Terry
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that converges?
Karl-Olav Nyberg
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that converges?
Karl-Olav Nyberg
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that converges?
bursejan@gmail.com
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that converges?
bursejan@gmail.com
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that
converges?
Mike Terry
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that converges?
Karl-Olav Nyberg
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that converges?
Karl-Olav Nyberg
10/7/17
Read Re: Can two series, both diverges, multiplied give a series that
converges?
William Elliot
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that converges?
bursejan@gmail.com
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that converges?
Karl-Olav Nyberg
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that converges?
bursejan@gmail.com
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that converges?
bursejan@gmail.com
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that converges?
Jan Bielawski
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that converges?
Karl-Olav Nyberg
10/7/17
Read Re: Can two series, both diverges, multiplied give a series that
converges?
William Elliot
10/6/17
Read Re: Can two series, both diverges, multiplied give a series that
converges?
William Elliot

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.