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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




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



