```Date: Oct 6, 2017 11:32 AM
Author: bursejan@gmail.com
Subject: Re: Can two series, both diverges, multiplied give a series that converges?

For two series {sn} and {tn} just definethe product series as {sn*tn}, note this is NOT:     sum_i^oo ai*bi      /* NOT the product */where sn=sum_i^n ai and tn=sum_i^n bi. Theabove is also not the Cauchy product.Here is the product of two harmonic series:sn      sn^21	11.5	2.251.833333333	3.3611111112.083333333	4.3402777782.283333333	5.2136111112.45	6.00252.592857143	6.722908163etc...It pretty much diverges, since sn < sn^2,and sn diverges. And its not sum 1/n^2.Am Freitag, 6. Oktober 2017 17:13:31 UTC+2 schrieb Peter Percival:> 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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