2:00 PM
(maybe some missed it)
It's marvellous.

@Chris'ssis looks hellatious

@meer2kat I don't know what "hellatious" is. I suppose it's something like "very nice". :-)))

nearly 5,000 views. holy snap crackle
hel·la·cious
[he-ley-shuhs] Show IPA
1.
remarkable; astonishing: They're raising a hellacious amount of money in taxes.
2.
formidably difficult: We had a hellacious time getting here in the blizzard.
@Chris'ssis woops hellacious, not hellatious

@meer2kat OK, thanks! :-)

$\tiny{\text{pfft... californians used "hella-" before it was cool}}$

2:04 PM
hahahaha

:-)

@MickLH that's hella cool.

@Chris'ssis have you been listening to some cool songs lately?

@Chris'ssis :D nice

2:06 PM
@Chris'ssis So wait let me get this straight? it's a sum... of sums of reciprocals of products?

@Chris'ssis :-O

@Chris'ssis it's also easier when de-obfuscated :) math.stackexchange.com/questions/754760/…

@MickLH Yes.

@GabrielR. it's always funny to me when math people use big words

@GabrielR. :-)

2:10 PM
4,911

@Chris'ssis we add a $1$ inside and it factors and undergoes mass cancellation ? :D

@Chris'ssis I don't know if it's a coincidence or a conspiracy though

@GabrielR. That limit I posted yesterday was posed in a journal a long time ago. (this is what my former professor told me)
brb

@Chris'ssis Well I'm glad I asked this yesterday, otherwise I couldn't have found the answer to your problem lol. It's funny in maths how knowledge you acquired by chance or unwittingly can prove very useful some time after :)

@Chris'ssis does it equal zero??

2:15 PM
@MickLH The limit is 1.

I can't read the LaTeX :P

@GabrielR. Indeed.

Well actually it's the conditions on the sums, I'm not sure how the ellipsis wants me to expand that progression

@r9m, hi!
haha!

@Chris'ssis pretty well... just got back from the park

2:17 PM
@r9m Damage done!

@Sush Helloa :D

@robjohn OK

@sush Helloa :D

I'll be back a bit later.

@Chris'ssis my turn to ask tricky limits. What is $$\prod_{n=0}^{\infty}(1+x^{2^n})$$ where $0<x<1$?

2:19 PM
I'll be front a bit later.

Damnit what is this limit hour?
integrateeeeeeeee

@GabrielR. that is not tricky, it's elementary. :-) $\displaystyle \frac{1}{1-x}$

Although I did learn the Polylogarithm today studying that Clausen function :)

@Chris'ssis Nice :)

@Chris'ssis right. Proof ?

2:22 PM
@Chris'ssis unless $|x| \ge 1$

Note $$P=\prod_{n=0}^{N}(1+x^{2^n})$$ and multiply both sides by $1-x$.

@Chris'ssis but you already knew the trick :P

@GabrielR. This is not a trick, it's something obvious. I knew this when I was in the middle school.

@Chris'ssis It's not obvious!

@Chris'ssis that's arguable. When my teacher asked our class this year to give away the trick, no one knew...

2:24 PM
@GabrielR. are you serious?

@Chris'ssis I am, and there was a Silver IMO medallist in the room.

@GabrielR. wow, interesting.

@AwalGarg, Hi!

@Sush hello
@MickLH hey

I'm looking at a practice test here for my combinatorics final today, and it says to "Find $D_5$." What might this refer to? I don't recall reading about it and I don't see it anywhere in the relevant sections of my textbook

2:26 PM
@GabrielR. Why are you a black square?

@AwalGarg sup

@MickLH cool

We did basic counting methods, generating functions, recurrence relations, and the inclusion-exclusion principle

@sawariya hey bro

@Sawarnik it seemed obvious to me. Anyway.

2:26 PM
@Chris'ssis Did you ever go to IMO?

@GabrielR. ORLY ? ;) perhaps he/she didn't care enough .. or thought its too trivial to answer :P

@Sawarnik No, I never dreamt of that.

@Chris'ssis Ah, why am I not intelligent like you :( Ok.

i get to watch furnace automation for 3 hours this afternoon

@Sawarnik Maybe you're even much more intelligent than me, but you need to work to get used to this stuff. That's all!
@Sawarnik to believe in yourself, to love what you do and never give up.

2:29 PM
Wow. Thanks!

@Chris'ssis Anyway, let me step the game up. (I'm sure @DanielFischer will be interested). Let $f,g: [0,1] \rightarrow \mathbb R$ be positive continuous functions. What is $$\lim_{n\to \infty} \frac{1}{n}\sum_{k=0}^{n-1}\sqrt{f(\frac{k}{n})+g(\frac{k+1}{n})}$$ ?

@Sawarnik .. its inappropriate of me perhaps to put it like that .. sorry

@Sawarnik because I do not emit.

@Sawarnik you need to consider yourself a very valuable person, able of reaching any peak.

@r9m Want a sum of floors question?

2:31 PM
maybe it would be okay.
to be a duck.
2

@Sawarnik okay .. :) I'll try

@r9m Inappropriate?

@AwalGarg, are you college student?

@GabrielR. Riemann sums? I'm bored with these ones.

$purple$

2:32 PM
@Sush no, and I do not want to be one

@r9m

@Chris'ssis of course. But you won't get away with this one so easily :P

@Sush but I am almost at the verge of becoming one

$4981$

@meer2kat Purple and 4981? What do you mean?

2:34 PM
@Sawarnik $purple$ because purple; 4981 is number of views on my post
i'm basically just watching cuz i wanna see it hit 5k

lol

@AwalGarg $awal$

@r9m You trying?

3

A and B are two $2\times2$ reals matrices. then $$\det \Big(A^2+B^2+(A-B)^2\Big)\ge 3\det(AB-BA)$$ well, it is seems interesting, but it is really hard to get started

i'm also having way too much fun with these dollar signs

2:35 PM

@AwalGarg :D
almost there guys. 4,990

@meer2kat which post?

@GabrielR. Well, one of the importan things in my humble opinion is to feel the problem. Then, after that you can work and make the proof more rigorous if you want to. The answer there is obvious. $$\int_0^1 \sqrt{f(x)+g(x)} \ dx$$

28

It's well known that many animated Disney movie parents (at least one of a set) die, were never in the picture, or started the movie already dead. Is this just a financial thing (like in Toy Story), or does Disney have any other reason for this? Some examples: Toy Story - Dad doesn't exist T...

not math related at all

@meer2kat i gave another view

2:36 PM
maybe it is math related

@AwalGarg <3 thanks
@user127001 make it math related. then it would be perfect

@AwalGarg, are you NRI?

@meer2kat anytime mis.
@Sush no

@AwalGarg,ok.

@Sush but why?

2:37 PM
4997
4998

@AwalGarg, sorry, i couldn't understand your high level English.

5000 cheers

@meer2kat congos

there should be a badge for that
hahaha

@Sush you got to be kidding

2:39 PM
@Chris'ssis Yes, the answer is clear but the proof requires a bit of mastery of real analysis techniques

@meer2kat I didn't know that site exists. I signed up. Seems interesting

@AwalGarg i've enjoyed it. i like all these sites. i also like the math educators one, skeptics, and the english language one a lot

@Sawarnik I am a Bad Boy

@meer2kat i like their respective chat rooms more

@AwalGarg eh not all are so active

2:41 PM
@meer2kat right

@meer2kat but, i see you are on stackoverflow...
@meer2kat you got coding skills?

@AwalGarg i was learning visual basic. the project is done now

Does someone know Economics here?

@AwalGarg i was using visual basic with CAD software. it was intense

2:43 PM
@meer2kat cool. Good to see girls interested in such projects

@Sush i know that $1 is useless. does that count? @AwalGarg i'm an engineering student. When is$CV>\Delta CS>EV?$@meer2kat woho, if my family wins over my thoughts, i would be one soon @Sush i before e except after c @AwalGarg nice @GabrielR. If I'm not wrong we need no mastery if you look at it like that $$\frac{1}{n}\sum_{k=0}^{n-1}\left|\sqrt{f\left(\frac{k}{n}\right)+g\left(\frac{k+‌​1}{n}\right)}-\sqrt{f\left(\frac{k}{n}\right)+g\left(\frac{k}{n}\right)}\right|$$ It should be a piece of cake from here. 2:44 PM @meer2kat ok, IIRC that is an english spelling rule, right? Is there any room for economics questions? Am really stuck here! By the way, I need to buy food for pets ... (they wait for me) :-( @Sush you can ask me What will i do in exam? Back later on. 2:46 PM @AwalGarg, Really, do you know economics? Please help me with$CV>\Delta CS>EV.$@Sush ok, what do i do with that now? When does that inequality hold? @Sush I would rather suggest you go to Area 51 and propose an economics site. Case1: Normal good @Sush And add that as an example question 2:47 PM Case2: Inferior good OK! Will I get answer then? @AwalGarg @Sush I assure Thanks!@AwalGarg @Sush anytime @AwalGarg yerp @AwalGarg, when I ask econ question at EJMR, I get abused! 2:50 PM @Sush what is EJMerr? They say that undergrads are not allowed here! Oh, so you are not from econ community!@AwalGarg Sorry. @Sush Okay, tell them, you are not one... lol Substituting$x\mapsto x\sqrt{2k/\pi}$$\sqrt{\frac2\pi}\sum_{k=1}^\infty\frac1{k^2}\int_0^1\cos\left(kx^2\right)\,\mathrm{d}x\tag{1}$$ Let's compute \begin{align} \sum_{k=1}^\infty\frac{\sin(kx)}{k} &=\mathrm{Im}\left(\sum_{k=1}^\infty\frac{e^{ikx}}{k}\right)\\ &=\mathrm{Im}\left(-\log\left(1-e^{ix}\right)\right)\\ &=-\arg\left(1-e^{ix}\right)\\ &=\arctan\left(\frac{\sin(x)}{1-\cos(x)}\right)\\ &=\arctan\left(\frac{2\sin(x/2)\cos(x/2)}{2\sin^2(x/2)}\right)\\ &=\arctan(\cot(x/2))\\ &=\frac{\pi-x}2\qquad\text{for }x\in(0,2\pi)\tag{2} 3 @Sush ofcourse i am not @Sush i am a physics guy O ya I can, but my questions reveal the truth!@AwalGarg Ok, i see. 2:52 PM Ok, now everyone, i have a fun math joke which I want to post here. Basic math knowledge is more that enough to understand @robjohn awesome I'm left now. @AwalGarg, more than enough. more that enough? @Sush but i want to warn, its mildly adult Haha, no one is Kid here! we know that sec^2x = (secx)^2 now, for fun, lets open the RHS sec^2x = s^2.e^2.c^2.x^2 2:55 PM @Chris'ssis gauche? sinistra? now, each one of s, e and x get cancelled and c cancels completely we get 1 = s.e.x read fast, i will delete that @Sush I AM! I can't understand it! @robjohn "Fifty ways to leave your lover" left? Though, I am copying it:D 2:56 PM @Sush Yup, it was not that nice. @DanielFischer or two languages, yes. Ok, Though, cheers for @AwalGarg @AwalGarg You should take training from Khallil, he's one-liners are awesome! Who is Khallil@Sawarnik? @Sush hey, i want to post that smiley as well @Sush hey, i want to post that smiley as well And, i don't know latex, i will come back with latex 3:00 PM @AwalGarg Its not latex. @Sawarnik what is not latex? @AwalGarg, That is not latex! It is image! just copy the Url, and upload!:D The image.' @Sush i was talking about the joke Ok! Miss Under Standing ! @AwalGarg @AwalGarg, we both are blues! @Sush yay, we hit the skies 3:02 PM PK is blue too. see the reddish @sawariya aka @Sawarnik -_- OK@Sawarnik @AwalGarg, you will not be able to remove your joke now! @Sawarnik, why PK is "DOOJ KA CHAAND"? @AwalGarg math.stackexchange.com/users/99916/khallil-benyattou He made some awesome hilarious one liners yesterday! @Sush its meant to stay there until the end of multiverse 3:05 PM @AwalGarg, what is multiverse? multi-universe @Sush multiple universes OK.! Still not getting the meaning! @Sush i got that now, you are indian as well! Google. 3:06 PM YA YA. @Sawarnik would you mind repeating some here? @AwalGarg, no Pakistani is going to ask you ever if you are NRI. No, I don't remember it exactly, so I won't spill! @Sawarnik, ya! it will be nice! Ok, bye. 3:07 PM Ek Shaam Khalil ke Naam. @Sush I want to eat Sushi. Sush. Sush. I like to say that, awesome name! @Sawarnik, haha! You love my name so much! K, bye. @Sawarnik, bye, good night! Sweet dreams! @AwalGarg, bye, Physisit! bye 3:12 PM How to compute this series on paper: m.wolframalpha.com/input/… @AwalGarg, just one question, where do you live? Which City? @Sush Delhi @AwalGarg, ok! I hope you are not a cop coming to arrest me Haha@! New word i learnt today was: multiverse 3:14 PM @Sush come back and learn more @Chris'ssis this is a good way to start, but there's still a long way to go @deostroll Memorize that\sum_{n=1}^{\infty }{{{1}\over{2^{n}}}}=1$$hehehe I just got my last calc test back :P I made the stupidest mistake, though. On the first step of an integration, I factored x^3+x as (x^2+1)(x+1) :( I have no clue what got into me. @Sawarnik you here? @Sush could you do the problem that day with Cauchy Condensation? 3:30 PM @GabrielR. did you see the computation of \sum\limits_{k=1}^\infty\frac{\cos(kx)}{k^2} above? @robjohn yes @Chris'ssis sent me a link to Clausen function @GabrielR. was that in chat or off? @robjohn in chat @GabrielR. I don't see it. :-( @robjohn oh sorry for the confusion I have not looked at chat.stackexchange.com/transcript/message/14990245#14990245 yet 3:36 PM @GabrielR. and there is the relationship to \mathrm{Li}_2 :-) Do folks here know how to view mathjax markup on an android browser? Searching for an online editor/viewer kind of app. Early??? WTF, I had rotary dial until I moved in '97. @robjohn why is Im(log( = arg( ? Well done though ! @GabrielR. \log(z)=\log(|z|)+i\arg(z) @GabrielR. just think of e^{x+iy}=e^x(\cos(y)+i\sin(y)) @Daniel Careful, you'll date yourself. 3:43 PM @Mike I'm off the dating market. @Mike I've never been attacked with a date... banana, yes... @robjohn ah yes, of course The Banana Incident of '92 Hi everyone!! I need a help to solve a linear algebra and geometry problem with matrices can anyone offer me help? 3:54 PM @Bel Can you define the notations you use ? @robjohn I got (2) like \displaystyle \int_0^{2\pi} x \cos nx \,dx =\pi \int_0^{2\pi} \cos nx \,dx \implies \frac{1}{\pi}\int_0^{2\pi} \frac{\pi - x}{2}\cos nx \,dx = 0 and \displaystyle \frac{2\pi}{n} + \int_0^{2\pi} x\sin nx \,dx =\pi \int_0^{2\pi} \sin nx \,dx \implies \frac{1}{\pi}\int_0^{2\pi} \frac{\pi - x}{2}\sin nx \,dx = \frac{1}{n}, so that \sum\limits_{n=1}^{\infty} \frac{\sin nx}{n} = \frac{\pi - x}{2} for 0 < x < 2\pi @GabrielR. which notation the |\cdots| operator or the Frobenius norm \|\cdots\|_F @Bel What is a circular set ? What is Y ? @GabrielR. Y is any given full rank matrix and I said circular set because of the form which is a distance to a point or a radius I meant the center of the circle not radius the radius is \epsilon c^* The \|\cdots\|_1 norm is the summation of the entries absolute values Now, I created another cute version of the previous series, namely$$\sum_{n=1}^{\infty} \frac{\cos(n)}{n^2 2^n }\$