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How come gas molecules don't settle down? If the earth's gravity exerts a net downward gravitational force on all air molecules, how come the molecules don't eventually lose their momentum and all settle down? How is the atmosphere is still miles thick after billions of years? What's a concise way to check that environment variables are set in a Unix shell script? How to install a dictionary (danish) in Texmaker how to get full path from fileupload using Javascript Show that $\sum_{n = 1}^\infty n^qx^n$ is absolutely convergent, and that $\lim_{n \rightarrow \infty}$ $n^qx^n = 0$ I'm having trouble with proving the following for my math study:  Let $x$ be a real number with $|x| &lt; 1$, and $q$ be a real number. Show that the series $\sum_{n = 1}^\infty n^qx^n$ is absolutely convergent, and that $\lim_{n \rightarrow \infty}$ $n^qx^n = 0$  I tried this:  $\sum_{n = 1}^\infty n^qx^n$ = $x + 2^q + 3^qx^3 + ...$ $= x(1 + 2^qx + 3^qx^2 + ...)$  So far, I don't know how I have to do this, I tried to apply the root test on this, but for that I would need to compute the lim sup of the series, so I thought that was not correct. Could you explain me how to prove this?  Thanks in advance! Why do people sometimes use the past perfect form of a verb when the past would suffice? (e.g. "you had mentioned") How prove this $\prod_{1\le i<j\le n}\frac{a_{j}-a_{i}}{j-i}$ is integer Fatal error: Call to undefined function add_action() - an untouched problem The question was asked many times in many ways, but unfortunately is not covered well in most of the answers. I'm having the same issue doing things using include-files.  In my TwentyFourteen child theme's functions.php I used:  require_once get_stylesheet_directory_uri() .'/admin-panel/theme-options.php';   And I'm using . I've used it in many of my projects, the same way mentioned here, without having the error. But recently I'm having the issue in several of my projects. If I take the code to functions.php then everything's fine. But it's occurring only when I'm trying to include/require external file.  I'm having the error:     Fatal error: Call to undefined function add_action() in C:\xampp\htdocs\project\wp-content\themes\my-theme\admin-panel\theme-options.php on line 2   In this case I'm having the error using a child theme (of T14). But even in one of my parent theme I'm facing the issue. But in the same environment my other projects are running well with all the includes and/or requires (where several add_action()s are defined). I'm having issues in ALL the add_action() calls, like CPT assigning, Custom Taxonomy assigning etc. But I'm successfully developing another two projects including external files from inc/ folder where all my CPTs are assigned and their meta boxes too.  I tried reinstalling WordPress, deactivating all my plugins, tried from Child Theme, tried only the same thing by modifying TwentyFifteen (applying default theme), tried require(), require_once(), include(), include, require_once, and require one after another with failure. And I'm using WP 4.1.1 in all the good and problematic installs.  Majority of the previous questions are answered with a simple line:     As the message says, you haven defined the function add_action() and yet you're trying to use it.   But,   how come (isn't it already defined by WordPress)? and why it's differing project to project in the same environment (How come it's out of the scope now only in particular project[s])? Need rtl8814au driver for kernel 5.3 on Ubuntu 19.10 MySQL Query GROUP BY day / month / year Do the beacon lighters really live on top of the mountains? Following this image I found online:    Do the beacon lighters really live on top of the mountains?  It seems really cold on top of some of these mountains and there are no villages or whatsoever. DSolve gets stuck on system of differential equations with unassigned variable Where does the word "torsion" in algebra come from? In how many different ways can we place $8$ identical rooks on a chess board so that no two of them attack each other? In how many different ways can we place $8$ identical rooks on a chess board so that no two of them attack each other?  I tried to draw diagrams onto a $8\times8$ square but I'm only getting $16$ ways.  Does that sound right?  Thanks for the help! What packages do people load by default in LaTeX? I'm getting the impression from reading the answers written by some of the real experts here that there are quite a few little packages that just tweak LaTeX2e's default behaviour a little to make it more sensible here and there.  Rather than try to pick these up one by one as I read answers to questions (and thus risk missing them), I thought I'd ask up front what LaTeX2e packages people load by default in (almost) every document.  As this is a "big list" question, I'm making it CW.  I don't know if there are standard rules across all SE/SO sites for such questions, but on MathOverflow the rule is generally: one thing (in this case, package) per answer.  I guess that if a couple of packages really do go together then it would be fine to group them.  This is perhaps a little subjective and a little close to the line, so I'll not be offended if it gets closed or voted down!  (But please explain why in the comments.)  Also see our community poll question: Reset the password in Ubuntu / Linux Bash in Windows I have installed Linux Bash on Windows 10 (available from Microsoft), but I've forgotten my password.  I've searched for a solution but I only find suggestions that involve doing something before the system boots, like accessing recovery mode, but that will not work in this case as this Ubuntu is just an application within a Windows system and doesn't have its own boot process.  How can I reset my password? I'm trying to split text in a JTextArea using a regex to split the String by \n However, this does not work and I also tried by \r\n|\r|n and many other combination of regexes. Code:  public void insertUpdate(DocumentEvent e) {     String split[], docStr = null;     Document textAreaDoc = (Document)e.getDocument();      try {         docStr = textAreaDoc.getText(textAreaDoc.getStartPosition().getOffset(), textAreaDoc.getEndPosition().getOffset());     } catch (BadLocationException e1) {         // TODO Auto-generated catch block         e1.printStackTrace();     }      split = docStr.split("\\n"); } Can a 20V 4.51A power supply be used with a computer that requires a 19V 3.42A power supply? Apache 2.4 - 403 HTTP status code What's the meaning "them" here?