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Tomasz Grysztar

Joined: 16 Jun 2003
Posts: 7756
Location: Kraków, Poland

Tomasz Grysztar

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.

08 Sep 2017, 18:43

YONG

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

YONG

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

09 Sep 2017, 05:05

tthsqe

Joined: 20 May 2009
Posts: 730

tthsqe

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]

09 Sep 2017, 08:25

YONG

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

YONG

tthsqe wrote:

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

Wow, you are super-smart!

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

Wink

09 Sep 2017, 09:48

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