$$\lim\limits_{n\to \infty}({2^n\over n!}+2) * {n^2+n\over 2n^2+1} $$ I know that $$lim_{n\to \infty}{n^2+n\over 2n^2+1} $$ is 0.5 and the limit to the first part is 0. Thus is the limit of the whole equation just 0?
Why is     $$\lim_{n \to \infty} \frac{2^n}{n!}=0\text{ ?}$$   Can we generalize it to any exponent $x \in \Bbb R$? This is to say, is     $$\lim_{n \to \infty} \frac{x^n}{n!}=0\text{ ?}$$     This is being repurposed in an effort to cut down on duplicates, see here: Coping with  duplicate questions.  and here: .
Mirror modifier. Mirrored half is not aligned, but rotated I was working on my character's hand when I realized half of the body was suddenly deleted. I am trying to recreate the other half, but it just won't mirror properly in the center. I tried moving the origin to the 3D cursor while it was completely centered, but the mirror modifier is still applied at an angle. Why do RAW images in Darktable have a lot of noise? I would like to connect a USB Mouse, Keyboard or Storage Device to my Nexus 4. So far I know, for this USB OTG must be supported. Unfortunately I can not find any actual information about this.  Does anybody know whether USB OTG is supported by Ubuntu-Touch? If yes, does anybody know if it would work with a Nexus 4 device? Why are my fields initialized to null or to the default value of zero when I've declared and initialized them in my class' constructor? Jawa asked me this  and I didn't know the answer. So I present it to the meta SO community:     [To get the Yearling badge] Do you need to earn the 200 rep within that one year or is it enough to get 200 at some point after being a member for a year? And does 'a year' mean the very first 12 months or the last (sliding window of) 12 months?    I would assume that if you hit 200 reputation after you've already been around for a year, then you would get the Yearling badge. But I don't know. How can I restart an app game from the beginning Can we clarify to the OP that their question is not yet closed and the duplicates are only suggestions? I keep seeing custom flags in the queue from question askers who are incredibly irritated because there is a big, prominent box at the top of their question. It's just a list of other questions which may have the answer they desire, and is only even displayed to them because the question is not closed yet.  This question may already have an answer here: [list]  But to an ordinary user, it is not at all clear that the box is only shown to them, or that it will go away on its own if their question never actually gets closed. Could the text for this notice be altered to make it more clear that:  They are just suggestions for the person to view. Potentially if they agree with one, they should vote to close their own question as a duplicate of it.  Their question is not closed yet. If they disagree with the duplicates suggested, they should clarify their question and explain why it's not a duplicate.   I was thinking of an altered wording such as:  You might be able to find an answer to your question here: [list] If those answers do not fully address your question, please [edit your question] to clarify your exact problem.  I went with a more direct wording for the bolded title. Since the notice is only displayed to the asker, it makes more sense to talk directly to them in the message rather than making it feel like it's supposed to be addressing the entire audience of the site. Emphasize that only that person is seeing it by talking to them. It would also be helpful to append a &quot;More info&quot; link at the end of the message that links them to some further documentation about duplicates, and explains how the notice works - particularly that it will go away eventually or change to a proper duplicate notice if the question does get closed. How can I selectively disable paste blockers How can I discover any USB storage devices and/or CD/DVD writers available at a given time (using C# .Net2.0).  I would like to present users with a choice of devices onto which a file can be stored for physically removal - i.e. not the hard drive. I accepted an answer to this question:    but the bounty was awarded by Community&thinsp;♦ to another answer. Why did this happen? Stopping xcode from indexing Embedding C++ Objects into QML with Context Properties According to Qt5 documentation:  all public slots of C++ classes that inherit from QObject, are accessible from QML Here what I did:  C++  class MyClass : public QObject {     Q_OBJECT  public slots:     void doStuffFromQmlSlot()     {         qDebug() &lt;&lt; Q_FUNC_INFO;     }  public:     MyClass()     {         qDebug() &lt;&lt; Q_FUNC_INFO;     } };   my main.cpp contains:  MyClass myClass; QQmlEngine engine; engine.rootContext()-&gt;setContextProperty( "myclass", &amp;myClass ); QQmlComponent component( &amp;engine, QUrl::fromLocalFile("qml/qtquick-01/main.qml") ); component.create();   QML  import QtQuick 2.0  Rectangle {     width: 360     height: 360     Text {         text: qsTr("Hello World")         anchors.centerIn: parent     }     MouseArea {         anchors.fill: parent         onClicked: {             myclass.doStuffFromQmlSlot();              Qt.quit();         }     } }   Actually the QtCreator seems to recognixe the exposed myclass object into the QML as it enables auto-completion of both class name (myclass) and the public slot doStuffFromQmlSlot(). When I run the application I unfortunately got the following error:  ReferenceError: myclass is not defined  Any clue on what I'm doing wrong? I have the following problem.      Let $f:D\to \mathbb C$ be a holomorphic function, where $D=\{z:|z|\leq 1\}.$ Let $$f(z)=\sum_{n=0}^\infty c_nz^n.$$ Let $l_2(A)$ denote the Lebesgue measure of a set $A\subseteq \mathbb C$ and $G=f(D).$ Prove that $$l_2(G)=\pi\sum_{n=1}^\infty n|c_n|^2.$$   After a long struggle I managed to come up with the following formula $$l_2(G)=\iint_D |f\,&#39;(z)|^2dxdy.$$ It looks like the right thing to use because $$f\,&#39;(z)=\sum_{n=1}^\infty nc_nz^{n-1},$$ which is similar to what I have to prove. I understand that the $\pi$ will appear when I integrate something over the angle $\phi$ in polar coordinates. But I don't know how to find the square of the absolute value of the right-hand side to even start integrating...  EDIT: The function is supposed to be  (one-to-one). (I'm not perfectly sure I'm translating the term correctly. The (Polish) word in the statement of the problem was "jednolistna". I have not met it before.) Can I still use logistic regression if some variables are not applied to all the observational units? Some of the variables are questions that are not being asked to every single person in the questionaire depending on how they answered previous question(s). So would I still be able to use a logistic regression if some of the questions (the independent variables) are only measuring the responses of SOME of the respondents? How to know if something is a primitive concept, a law, a definition or a theorem Some basic Physics books are often misguiding in the sense that they don't make clear whether something is a primitive concept, a law, a definition or a theorem. This is often a little confusing. I've asked here some moments ago if there's a definition of force, and I've been redirected to a question about whether Newton's Laws are laws or definitions of mass and force.  This is just an example, but there are many others, like for instance, the conservation of energy, which some books present as a theorem, and some places says that this is a law of Physics. Time on the other hand, is something that according to Feynman's lectures on Physics, cannot be defined, so we just say how to measure it and leave it as a primitive concept.  In this context: how in general can we identify whether something is a primitive concept, a fundamental law of Physics, a definition or a theorem? Example where union of increasing sigma algebras is not a sigma algebra Site.createPortalUser() returning null in test context How to get a file's Media Type (MIME type)? How do I translate an ISO 8601 datetime string into a Python datetime object? I use netstat to check my port status.  I was wondering what's the difference between port status LISTENING, TIME_WAIT, CLOSE_WAIT, FIN_WAIT1 and ESTABLISHED?