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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 7, 2017 12:43 AM


On Fri, 6 Oct 2017, 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? > > > It is the multiplication of the two series.
> > That doesn't answer Peter's question. Each series has infinitely > > many terms, and you need to say what you mean the product to be > > calculated from those terms. > > > > To get you started in the right direction, suppose the first > > series is: > > Sum [n=1 to oo] (a_n) > > > > and the second is: > > Sum [n=1 to oo] (b_n) > > > > Now, what do you mean by the "product" of these series? > > There are two ways to give the product: > 1: sum(a) * sum (b) = sum (c) or > 2: every of sum a multiplied with the ones of sum of b. > If the sum of any of them is not (in 2) as we like, then none of > them are!
None of that makes any sense.



