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Tomasz Grysztar
Assembly Artist


Joined: 16 Jun 2003
Posts: 6633
Location: Kraków, Poland
Math on board
I have experimentally enabled support for [tex] tags with LaTeX syntax on the forums. I'm going to leave it on unless it causes any problems. If you would like it to stay, please do not abuse it.
Post 08 Sep 2017, 18:43
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YONG



Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
Define:

T(n) = \sum_{i=1}^{n}  t_i

and

G(n) = \sum_{i=1}^{n}  g_i

and

TG(n) = \sum_{i=1}^{n}  (t_i g_i)



Given that:

\lim_{n \to \infty} T(n) = \infty

and

\lim_{n \to \infty} G(n) = \infty



Is it possible to have \lim_{n \to \infty} TG(n) = 0 ?

If yes, give an example; if no, explain why not.

Wink
Post 09 Sep 2017, 05:05
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tthsqe



Joined: 20 May 2009
Posts: 701
Yong, this is trivially easy if you let the even-indexed t_i be zero and the odd-indexed t_i be the term of your favourite divergent series, and vice-versa for the g_i.

I think as long as furs and systemerror dont find out about them, the tex tags will not be abused. Thanks again Thomasz.[/code]
Post 09 Sep 2017, 08:25
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YONG



Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E

tthsqe wrote:
Yong, this is trivially easy if you let the even-indexed t_i be zero and the odd-indexed t_i be the term of your favourite divergent series, and vice-versa for the g_i.

Wow, you are super-smart!

BTW, it is "YONG", not "Yong".

Wink
Post 09 Sep 2017, 09:48
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