Is taking the lim of the series the same to taking the series of the lims?
Under what condition we can interchange order of a limit and a summation?
I have an issue with my website: Google isn’t using my meta description, instead it’s using the content of the web page and I’m really confused.  Reason I’m confused is because I have checked and I don’t have duplicate page titles, description nor keywords, neither do I have any robots.txt for my website. My page title, description and keyword is unique, and page description is about 150 characters.  I have my site in Google Webmaster Tools and I checked for errors, but found none.  So I really don’t know why Google Search isn’t using my meta description. How can I apply an effect when a player left-clicks/right-clicks with an item in hand? Is there a way so that I make make it when I left click/right click with a certain item it applies an effect? I know that you can apply attributes to wearing armor and things but I want it so when you use the item it applies an effect on your player.  For example, let's say I want something so that when I right click with a certain item (let's say an iron ingot that was given to me) I'll then have a jump boost for 10 seconds. So kinda like a potion in a way.  Is this possible with command blocks/commands/any mods? How do you tell what brand/make/model of bike I have? I have a bike I'm trying to sell because it's just been sitting in my basement. It looks as if someone primered it and the only thing I found was a serial number. Is there like a website I can look up more info on the bike using just that number? Visual Studio: How to break on handled exceptions? I would like Visual Studio to break when a handled exception happens (i.e. I don't just want to see a "First chance" message, I want to debug the actual exception).  e.g. I want the debugger to break at the exception:  try {    System.IO.File.Delete(someFilename); } catch (Exception) {    //we really don't care at runtime if the file couldn't be deleted }   I came across  notes for Visual Studio.NET:     1) In VS.NET go to the Debug Menu >>   "Exceptions..." >> "Common Language   Runtime Exceptions" >> "System" and   select "System.NullReferenceException"      2) In the bottom of that dialog there   is a "When the exception is thrown:"   group box, select "Break into the   debugger"       3) Run your scenario. When the   exception is thrown, the debugger will   stop and notify you with a dialog that   says something like:              "An exception of type "System.NullReferenceException" has   been thrown.              [Break] [Continue]"       Hit [Break]. This will put you on the   line of code that's causing the   problem.   But they do not apply to Visual Studio 2005 (there is no Exceptions option on the Debug menu).  Does anyone know where the find this options dialog in Visual Studio that the "When the exception is thrown" group box, with the option to "Break into the debugger"?  Update: The problem was that my Debug menu didn't have an Exceptions item. I customized the menu to manually add it. Conditionally run a view if another view has no results What makes some laser beams visible and other laser beams invisible? Programmatically obtaining Big-O efficiency of code I wonder whether there is any automatic way of determining (at least roughly) the Big-O time complexity of a given function?  If I graphed an O(n) function vs. an O(n lg n) function I think I would be able to visually ascertain which is which; I'm thinking there must be some heuristic solution which enables this to be done automatically.  Any ideas?  Edit: I am happy to find a semi-automated solution, just wondering whether there is some way of avoiding doing a fully manual analysis. I'm trying to create a multi-page table with all cells having the same height (as well as certain fixed widths) so that certain manual cut-and-paste operations are a lot easier.  One issue is that one column in particular is text-heavy and should line-break within the cell.  As I don't want it justified, I looked into alternatives such as .  This is doing exactly what I want for horizontal alignment.  For vertical alignment, I've looked at  and the \vphantom method detailed in the above link doesn't seem to be working.  Here's what I'm currently working with:  \documentclass[11pt]{article} \usepackage{array}  \newcolumntype{P}[1]{&gt;{\raggedright\hspace{0pt}\arraybackslash}p{#1}} \def\Z{\vphantom{\parbox[c]{1.7in}{\Huge Something Long}}}  \begin{document} \begin{tabular}{| c || P{0.5in} || P{0.5in} || P{5in} |}\hline  1.  \Z &amp;&amp;&amp; Long long long long long long long long long             long long long long long long long text  \\\hline 2.  \Z &amp;&amp;&amp; More long long long long long long long long             long long long long long long long text  \\\hline \end{tabular}   When I compile, the cells do not have a uniform height, and none of them are as large as 1.7 inches vertically.  So this suggests that somehow the \vphantom method is failing.  Does anybody know of a relatively straightforward solution to this problem? What is the rule for omitting/including the definite article in the following sentences:     I used to play piano.   I used to play the piano.   I would pick the first sentence, but I've heard people say the second sentence even when they are not referring to a specific piano. Which one is correct? Is there a way to assign a value to a variable, that value which we get in terminal by writing any command?  Example command: sensors  From that we get CPU temperature. How can I assign this value to a temp_cpu variable? I want to install Skype, but I can't locate it in Software Center or by using Synaptic Package Manager. Can anyone help me? Given that   $x^x = y$; and  given some value for $y$   is there a way to expressly solve that equation for $x$? How do you end with a single quote followed by a double quote? Size of files in Windows OS. (It's KB or kB?) In Markov inequality proof, why is $\int_a^\infty xp(x) \, dx \ge \int_a^\infty ap(x) \, dx$ Markov inequality,   $$\Pr(X \ge a) \le \frac{E[x]}{a}$$  Proof  $$\begin{aligned}      E(X) &amp;= \int_0^\infty xp(x)\,dx = \int_0^a xp(x)\,dx + \int_a^\infty xp(x)\,dx \\       &amp;\ge \int_a^\infty xp(x)\,dx \ge \int_a^\infty ap(x) \, dx  \end{aligned}$$  Why is the last inequality true? Why is it ok to change $x$ to $a$, and we know it is less than or equal to? How did they figure it out? Thanks! I am travelling from Singapore to San Francisco and the airline has a layover of 7.5 hours at Tokyo Airport (NRT). I am wondering if I would be allowed to go out to experience the city for a while in some form a visitor visa.  I know Singapore has such facilities, but does anyone know if I can do it in Tokyo? Any suggestions or pointers are welcome. Note - I do not have a visa for Japan yet, but I am hoping that 1 day visitor visa could be possible at airport. How can I execute a terminal command (like grep) from my Objective-C Cocoa application? I'm working with some code that widely uses the idiom of returning a pointer to a static local variable.  eg:  char* const GetString() {   static char sTest[5];   strcpy(sTest, "Test");   return sTest; }   Am I right in thinking that this is safe?  PS, I know that this would be a better way of doing the same thing:  char* const GetString() {   return "Test"; }   Edit: Apologies, the function signature should of course be:  const char* GetString(); Under what circumstances will a passive HDMI-to-VGA adapter work? I have bought a no-brand, passive HDMI Male to VGA Female adapter, to link up a PC with a more dated monitor. It did not work.  After doing some reading, I have learned that buying such an adapter is often discouraged because in many cases it will not convert the signal from Digital to Analog, or the Motherboard/CPU on a specific computer might not be compatible with that particular adapter.   So my question is: seeing how there are so many of these passive adapters on the market, are there circumstances under which they actually do suffice to connect an HDMI output to a VGA input? Or are they generally just a rip-off?  Example of the kind of adapter I bought: I want to install selenium webdriver in my Ubuntu 16.04 system for python