What is the probability that he will sit on his/her seat?
Taking Seats on a Plane
Git ignore file for Xcode projects Convergence of Ratio Test implies Convergence of the Root Test In Elias Stein and Rami Shakarchi's Complex Analysis textbook, we have the following exercise:     Show that if $\{a_n\}_{n=0}^\infty$ is a sequence of complex numbers such that $$\lim_{n\to\infty}\frac{|a_{n+1}|}{|a_n|}=L,$$ then $$\lim_{n\to\infty}|a_n|^{1/n}=L.$$    I've been trying to prove this with no luck. The only thing I've thought of doing is $$\lim_{n\to\infty}\left(\frac{|a_{n+1}|^n}{|a_n|^n}\right)^{1/n},$$but this hasn't lead me anywhere except dead ends. Will someone provide a hint for me about how to proceed? Thanks!  Minor update: I don't know if it's helpful yet, but I know we can write the limit as $$\lim_{n\to\infty}\left(\frac{|a_{n+1}a_n\cdots a_0|}{|a_n\cdots a_0|}\cdot\frac{1}{|a_n|}\right).$$This reminds me a lot of the geometric mean, which even has the exponents I'm trying to get... Fish vs Fishes for plural use Now, I encountered a sentence in a text book, saying     Many fish are specially adapted to live only in certain places.   I know that plural of the word fish can be fish as Merriam says    But wouldn't it someway or somewhat sound unusual or "too unique"?  Is it only to me? I am having some issues when rendering an image, my rendering screen is turning into grey even when making a full render. What am I doing wrong? According to :     The electron has no known substructure. Hence, it is defined or assumed to be a point particle with a point charge and no spatial extent.   Does point particle mean the particle should not have a shape, surface area or volume?  But when I searched Google for the "electron shape" I got many results (like  and ) that says electrons are round in shape. Why can't I transform faces, edges, or vertices without transforming the whole object? My problem is that I sometimes lose the ability to independently translate or otherwise transform any parts of a single mesh. If I try, for example, to just translate several faces, edges, or vertices, then the entire mesh will stretch and displace itself in order to follow the translation. Or, alternatively, if I try to translate just one face then the whole mesh will move as if I'm translating in Object Mode.  I'm not really sure I know how to describe this problem properly. I don't even know how to reliably reproduce it. It seems to happen to any given mesh at random, and it doesn't stop happening to that mesh unless I delete and remake it.  I assume that I must be doing something wrong to cause this to happen. Does anyone have any ideas? Thanks. If diary Tom Riddle had succeeded, would there have been two Voldemorts? Schwarz's Lemma and functions with positive real part Problem:     Let $D = \{ z \in \mathbb C : |z| &lt; 1 \}$. Suppose $f : D \to \mathbb C$ is a non-constant analytic function such that $\mathrm{Re} f(z) \geq 0$ for all $z \in D$.      (a) Show that $\mathrm{Re} f(z) \neq 0$ for all $z \in D$.      (b) Using a Möbius transformation and Schwarz's lemma, prove that if   $f(0) = 1$, then $$ |f(z)| \leq {1+|z| \over 1-|z|}. $$   What can be said if $f(0) \neq 1$?      (c) Show that if $f(0) = 1$, then $f$ also satisfies $$ |f(z)| \geq {1-|z| \over 1+|z|}. $$   Progress:  (a) We can use the open mapping theorem.  (b) We can compose a Möbius transformation $m$ that sends the right-half plane to $D$ with $f$. Then $h = m \circ f$ satisfies the hypotheses of Schwarz's lemma by construction. Simple manipulations of the inequality from Schwarz's lemma give the result.  (c) Looking at part (a), we know that $\mathrm{Re} f(z) \neq 0$, and so $f(z) \neq 0$. Thus, we can use the function $g = 1/f$ in the statement of part (b).  Question:  What about when $f(0) \neq 1$? I don't think you can get anything from $f(z)-f(0)+1$ unless $\mathrm{Re} f(0) &lt; 1$. And you can't in general rearrange the inputs of $f$ because $1$ isn't necessarily in the image of $f$. Also, I don't think you can get anything from $f(z)/f(0)$ unless $f(0)$ is real, because otherwise the range of $f(z)/f(0)$ could extend into the left-half plane. What limitations does converting question links to links with titles have? On this  there are more than 50 links to Stack Overflow questions. However, the last 6 links aren't converted to titles (http://facebook.stackoverflow.com/questions/6530420/control-the-image-that-facebook-shows-when-i-like-a-url should be converted to ).   However:  all http://facebook.stackoverflow.com/... into http://stackoverflow.com/... fixes this, both in the preview and the final result. Also, the preview won't show any title for http://facebook.stackoverflow.com/... links.  My question is, what limitations does this converting have? How are these question titles retreived? Via API? Through database?  I'm not sure about title, feel free to edit that I've been trying to change the language of my LaTeX document by replacing \usepackage[swedish]{babel} with \usepackage[english]{babel} but I only get this message:  ! Package babel Error: You haven't loaded the option swedish yet.   I've read in an other question at this forum that compiling enough would solve the problem, but that doesn't work for me. Does anyone know what I should do? Ubuntu touch - remote access to device in our company we developed an android app installed on nexus 7 tablets and on tablet we release to several customers. This app stays in foreground active 24/7 but we have problems in monitoring  the devices due to the restrictive access policies of unrooted Android devices.   We can't for example reboot the device remotely.  We are evaluating the possibility of installing Ubuntu touch to replace android on this tablets. Does Ubuntu touch offer more freedom for the remote access of the device? May I do remotely everything I could do normally with the tablet?   Moreover, are the apps developed with ubuntu sdk stable enough to run 24/7?  Thanks How do I need to configure SMTP Auth? I have dedicated FreeBSD box, The email sending without  is working perfectly but very slow. The receiver receives email after almost 15 mins. I checked the maillog it says delays and timeouts that means the server keeps on trying to send email again and again until it successfully sends one. This is consuming lots of CPU.  I am seeking help for configuring smpt module to use my dedicated box's  smtp server, I need help in following places where I have ???? sign:  #SMTP server settings SMTP server -&gt; smpt.mydomain.com  # Tested by pinging, its working SMTP backup server -&gt; mail.mydomain.com  # Also verified by Ping SMTP port -&gt; 25 USE SSL  #SMTP Authentication Username -&gt; ??????? Password -&gt; ???????   I tried using localhost, also username and password of the dedicated box or leaving both lines blank which gives me:     Unable to send e-mail. Contact the site administrator if the problem   persists.   also checking the debug log doesn't show any log, it says check admin/reports/dblog but when I got to the link it just shows me the contents from admin/reports no any dblog has the following ability:     Whenever a creature you control with a +1/+1 counter on it dies, return that card to the battlefield under your control at the beginning of the next end step.   I had a number of creatures on the battlefield, including Marchesa herself, with one or more +1/+1 counters on them when  was played, destroying each creature on the board.  When Marchesa and several other creatures would be killed simultaneously,   Does Marchesa's ability trigger for herself? Does Marchesa's ability trigger for the other creatures under my control with +1/+1 counters?   In attempting to resolve the issue, we tried to look things up, leading to , which cites Rule 603.6d as proving that Marchesa's ability should trigger both for herself and for each other creature with +1/+1 counters.  Unfortunately, none of us could actually understand Rule 603.6d, aside from this example:     Two creatures are on the battlefield along with an artifact that has the ability Whenever a creature dies, you gain 1 life. Someone plays a spell that destroys all artifacts, creatures, and enchantments. The artifacts ability triggers twice, even though the artifact goes to its owners graveyard at the same time as the creatures.   The example certainly seems analogous to me, but without understanding the actual rule, rather than just the example, we weren't too sure.  A complete answer has to not only answer the question, but back up that answer with citation and explanation of the official rules on the matter. Advanced format partition alignment I cloned a non Advanced Format drive (W7 64bit) to a new hard drive (Seagate) that was AF, the software I used supposedly does not support 4k very well (Todo Backup Free 3.5).   Is there a Windows utility to check alignment? I know of the Western Digital tool but not sure if it works on Seagate brand drives. If the partitions are not aligned, Am I better to clean install W7 64bit or do the partition alignment procedure? If so, Why?   It seems to be running fine so far. From what I have read Seagate drives use  technology to help with misaligned partitions on the fly, might explain why it runs well for me, but would still like to have the partitions aligned properly.  EDIT: Here is the diskpart output for my disk partitions  DISKPART&gt; list partition    Partition ###  Type              Size     Offset   -------------  ----------------  -------  -------   Partition 1    Primary            188 MB    31 KB    Partition 2    Primary            698 GB   188 MB In an urn there are $n$ red balls and $m$ blue balls. I extract them without replacement. Let $X$=time of first blue. What is $E(X)$?  I found PMF of $X$ and it is, if $k &gt; n+1$  $$P(X=k) =\frac{n(n-1) \dots (n-k+1)m}{(m+n)(m+n-1) \dots (n+m-k+1)}$$  How could I evaluate $E(X)$?  Edit: I'm looking for an explicit form of $E(X)$ Drawing line less than one pixel thick requires anti-aliasing in Android 4.2 How to access the Keyboard Layout Options in 13.10+ How can I have colored and underlined links with hyperref? I would like the internal hyperlinks generated by  to be colored and underlined.    Reading some of the package documentation, I know that these \hypersetup keys exist:   colorlinks: when true, color the link; when false, draw a border around the link and color that. linkcolor: the color of the link (requires colorlinks=true to have any effect) linkbordercolor: the color of the link border color (requires colorlinks=false to have any effect) pdfborderstyle: keys for the pdf borderstyle dictionary.  I don't know what keys and values exist for this dictionary, but I do know that pdfborderstyle={/S/U} or pdfborderstyle={/S/U/W 1} can change the link border from a box to an underline.   But it seems impossible with this key structure to have colored links (requiring colorlinks=true and colored borders (requiring colorlinks=false.)  Here is a minimal (non)-working example ():  \documentclass{article} \usepackage{xcolor} \usepackage{hyperref}  \hypersetup{colorlinks=false,linkbordercolor=red,linkcolor=green,pdfborderstyle={/S/U/W 1}}  \begin{document} \section{To See}\label{tosee} \vskip2cm \hyperref[tosee]{just to see} \end{document}   With colorlinks=false (the default), the text is black and the border is red.  With colorlinks=true the text is green and there is no border. Radius of Convergence when using Series[] "With what [...]?" or "What [...] with?" Making a comparison with Who/Whom I now have a question about the use of what with prepositions in questions. I'll explain by example:  These two sentences are correct, one is more formal than the other:  Who/Whom     Formal: With whom are you doing that? Informal: Who are you doing that with?   But if I substitute Who/Whom with What, the "formal" one sounds a bit awkward and I'm not sure if it's correct or not:  What     With what are you doing that? What are you doing that with?   So, are those last two questions grammatically correct? Is one more formal than the other?