## 5891 Reputation

19 years, 246 days
Munich, Bavaria, Germany

## Limits for sequences: Example...

Maple

With a member of the community I had some discussion about using Maple for limits of sequences.

The specific task was about F:=4*sqrt(n)*sin(Pi*sqrt(4*n^2+sqrt(n))) and limit F for n --> infinity for integers, which is asserted to be Pi, see https://math.stackexchange.com/questions/2493385/find-the-limits-lim-n4-sqrtn-sin-pi-sqrt4n2-sqrtn.

For moderate size of integers n it can be 'confirmed' by numerical evaluations. Formally it is not 'obvious' at all.

limit(F, n = infinity) assuming n::posint;

undefined

This is 'explained' by the help about assuming/details:

"The assuming command does not place assumptions on integration or summation dummy variables in definite integrals and sums, nor in limit or product dummy variables, because all these variables already have their domain restricted by the integration, summation or product range or by the method used to compute a limit. ..."
The help continues with suggestions how to treat the situation.

Which means that the limit is taken in the Reals, not in the discrete Naturals.

A more simple example may be limit(sin(n*Pi), n = infinity) assuming n::posint which returns "-1 .. 1".

But here we go:

MultiSeries:-asympt(F, n):
simplify(%) assuming n::posint: collect(%, n); #lprint(%);
limit(%, n=infinity);

O(1/2048*Pi^3/n^(5/2)) + Pi -1/96*Pi^3/n - 1/16*Pi/n^(3/2) + 1/30720*Pi^5/n^2

Pi

As desired.

## site seems to work now with FF...

`The board is going to work now with FF for me after latest updates.NB: I got some mails advicing to delete (old) cookies for Mapleprimes, butas my browser is alsways completely cleared on close (or on demand) that cannot have been the reason.It works at least, if I give up all security settings. Which I do not want,so I sketch a way to use them.Be aware that not all in a page comes from Mapleprimes. Some is from anotherserver maplesoft.com and thus considered as 3rd party. Same for some scriptsand CSS etc, which stem from Google, jquery (or else)If using NoScript or some blockers or similar essentially one has to allowajax.googleapis.com, which was needed in the previous version as well (seebelow). Dito code.jquery.com is needed (both are 3rd party to Mapleprimes).It still may hang up at loading ajax-loader.gif, which is located on theserver mapleprimes.com - I do not know why. After allowing a request policyfrom mapleprimes.com to ajax.googleapis.com it loads.That allows to still block all the social media stuff (especially FB connectis disabled)And currently I do not see calls to 2o7, just Omniture is trying to work.---For the call to Google: it seems to be needed only for their jquery library,ajax.googleapis.com/ajax/libs/jquery/ and .../jquery/.But the site calls the open source code.jquery.com/ui anyway. So why usingGoogle as well? Why not change and stay on code.jquery.com?Calling to Google transmits my IP and browser header, it is like a fingerprintand allows GG to identify me later on as Maple user. I dislike that very much.Edited: edit works as well`

## still not working with FF...

After disabling all security addons the Ajax gif loads, then it shows an error and after that it jumps to a page displaying "2013", but that page actually does not have any content (use ctrl + u to see it).

And the I see, that the browser tries to load from maplesoft.112.2o7.net and hangs up in that transfer (have not checked the ports).

In reality I would forbid to load from 2o7, as I receject almost all trackers.

Every reasonable person aware of security and xss forbids dubious sources from other websites (and I am not happy that this sites call Ajax at Google)

And if that is the reason for the bad behaviour of the new sites it would be a good joke, really.

For me it only works with IE and all its security issues (and I have to use "preview" before posting is possible)

MaplePrimes

I can post answers, but those are not shown

PS: would have done at other threads - but as alreyd said ...

PPS: how about testing? grrrrrrrrrr .......

## "Is this matrix primitive?": just an ide...

Since it is not possible for me to reply directly in that new Maple Primes:
I branched. Feel free to re-join for a reasonable structure. What a mess.

http://www.mapleprimes.com/questions/145527-Is-This-Matrix-Primitive

I am rusty on such (may be it is 'obvious' via Lie theory). Your group is just the
group of invertible matrices over the integers (this follows from algebra). And as

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