If I flip an unbiased coin an infinite number of times, what is the probability that, at some point, the number of heads will be twice the number of tails?  I have already tried making a branching probability tree, but I just get overwhelmed and it seems to go on forever... I don't know how to reconcile it.
I gave my friend  as a brainteaser; while her attempted solution didn't work, it raised an interesting question.  I flip a fair coin repeatedly and record the results.  I stop as soon as the number of heads is equal to twice the number of tails (for example, I will stop after seeing HHT or THTHHH or TTTHHHHHH).  What's the probability that I never stop?  I've tried to just compute the answer directly, but the terms got ugly pretty quickly.  I'm hoping for a hint towards a slick solution, but I will keep trying to brute force an answer in the meantime.
How to transit through Delhi without a visa? I have read a lot on this subject on the Lonely Planet forum and it looks like the staff on ground can transfer your bags through the Delhi airport if you have a connecting flight without you having to go out to check them in again and therefore needing a visa. I refer of course to the situation when you go with 2 different airlines, because otherwise the luggage is transfered automatically.  I posted a  and mentioned it briefly there, however I think this subject deserves a separate question and a detailed answer.  Does it depend on the type on an airline? I have read that Jet is no problem, what about AirIndia and IndiGo? And what about the incoming flight to Delhi from Europe or USA, do they all can hand over you luggage to the Indian airlines and pick it up again on the way home? Do you have to contact them before and explain your situation? Or check in your luggage directly to your desired destination? The site still thinks it's attached to Stack Overflow When is 6 a square in Zp To find when $6$ is a square I divided $6$ in to $2$ and $3$ by The Legendre symbol.  $$\frac{6}{p} = \frac{2}{p} \times \frac{3}{p}$$  I know that we can multiply the cases of when $2$ and $$ are squares because then it is (1)(1) by Legendre.   $2$ is a square when $p \equiv 1 \pmod{8}$   $3$ is a square when $p \equiv 1 \pmod{12}$  so $6$ is a square when $p \equiv 1 \pmod {24}$ ($96$, but the $lcm(8,12)= 24$)   but how do I find the cases when $2$ and $3$ are both NOT squares? because then $6$ would be a square then as well, $(-1)(-1) = 1$ by Legendre. Prove that $||x|-|y||\le |x-y|$ Undo a particular commit in Git that's been pushed to remote repos How do you find out your very first chat in a particular chatroom? I want to know my very earliest/first chat post in a chatroom. Is there perhaps a way to search/view all my posts and sort the results? Comma usage with compound sentences {actually compound predicates as per Rob's answer} Rule 101 of compound sentences is that a coordinate conjunction must be accompanied by a comma most of the time when joining independent clauses, yet I stumble across sentences all that time that seem to abuse this rule. Normally, it's a case of the subject not being present in the second clause, as in the following example:      "They usually start out as an abbreviation, but turn into acronyms   when they become well known."   (taken from the Oxford Style Manual)   To me, this comma cannot be correct because the clause after the comma doesn't contain a subject and therefore cannot be independent (right?). As far as I'm concerned, it's not the 'Comma to set off a contrast rule because I can find plenty of other where 'and' is used and the subject's missing in the second clause.  what's the deal here?   Thanks in Advance for any responses I may receive! I am trying to install Linux headers for Kali Linux on my machine and I have tried every possible solution on the internet but it always show "Unable to locate packages "  root@kali:/usr/sbin# apt-get install linux-headers-4.6.0-kali1-amd64 Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package linux-headers-4.6.0-kali1-amd64 E: Couldn't find any package by glob 'linux-headers-4.6.0-kali1-amd64' E: Couldn't find any package by regex 'linux-headers-4.6.0-kali1-amd64'   Here is my sources.list file :  # Regular Repositories deb http://http.kali.org/kali sana main non-free contrib deb http://security.kali.org/kali-security sana/updates main contrib non-free # Source repositories deb-src http://http.kali.org/kali sana main non-free contrib deb-src http://security.kali.org/kali-security sana/updates main contrib non-free   Uname -a output :   root@kali:/usr/sbin# uname -a Linux kali 4.6.0-kali1-amd64 #1 SMP Debian 4.6.4-1kali1 (2016-07-21) x86_64 GNU/Linux Rescuing/Compiling old TeX file starting with “\input amstex” I have come across an ancient (1995) LaTeX file which was (surely) once compliant, but now does not compile at all. Is there any way to rescue it?  My actual question is much more precise. I want a copy of the follow paper on the arXiv:    Downloading the pdf source produces something which looks like a document on a4 paper printed on US letter (the bottoms of some pages are cut off). However, if you download the TeX source from the arXiv, then it doesn't compile (even adding .tex, naturally). I'm using an up to date version of TeXshop on a mac. I am working on a website for a client, and even though the site ranks extremely well for various different keywords (which is good), if I search for the site's name the homepage does not appear even on the second page on Google. I have to add the .com so it will appear.  But, for big brands like Best Buy, Nike and millions of others it is enough to just search for the brand itself and the first or second suggestion on Google is the brand's homepage.  How can I raise my brand's authority in Google so it will appear in Google on the first page when some searches for it?  I have tried changing the breadcrumbs so instead of "HOME" it is now the brandname, linked to the homepage. I thought that it will help with internal linking if the anchor text is the brand's name instead of the word "HOME".  Any ideas please? Can I completely disable Cortana on Windows 10? Are logs kept for past at jobs? Asymptotic expansion for Fresnel Integrals If you take the fresnel integrals to be $$S(x) = \int_{0}^{x}\sin \left(\frac { \pi \cdot  t^2}{2} \right) dt$$ How do you find the asymptotic expansion? I know it begins with a $1/2$ but how? I need a good explanation (references are a plus) on Python's slice notation.   To me, this notation needs a bit of picking up.   It looks extremely powerful, but I haven't quite got my head around it. Introduction to statistics for mathematicians What is a good introduction to statistics for a mathematician who is already well-versed in probability?  I have two distinct motivations for asking, which may well lead to different suggestions:   I'd like to better understand the statistics motivation behind many problems considered by probabilists. I'd like to know how to better interpret the results of Monte Carlo simulations which I sometimes do to form mathematical conjectures.   I'm open to the possibility that the best way to go is not to look for something like "Statistics for Probabilists" and just go to a more introductory source. Testing convergence of series $\sum_{n=3}^\infty\frac{1}{n (\ln(n))^p(\ln\ln(n))^q}$ Lets have this problem. $$\sum_{n=3}^\infty\frac{1}{n (\ln(n))^p(\ln\ln(n))^q}$$ I have rewritten this to a form $$\sum\frac{1}{np'^{\ln\ln(n)}q'^{\ln\ln\ln(n)}}$$ For $p,q\in\mathbb{R}$. Obviously, $p',q'&gt;0, p=\ln(p'),q=\ln(q')$ Inequality involving the sup of a function and its first and second derivatives How to remove local (untracked) files from the current Git working tree How do you delete untracked local files from your current working tree? What is the need of acceleration? As we can usually predict the various forces that a body might be undergoing based on its position and its velocity.Hence what is the need of acceleration? 1-1 correspondence between [0,1] and [0,1)