Why is $\sum_{n=0}^{\infty }\left ( \frac{1}{2} \right )^{n}= 2$?
Values of $\sum_{n=0}^\infty x^n$ and $\sum_{n=0}^N x^n$
How do I remove XFCE from my computer? My computer is overheating because I got too many desktop environments installed like: MATE, Cinnamon and XFCE.  I uninstalled them, but XFCE failed to uninstall. I get this error.   sudo apt-get purge xfce4     Reading package lists... Error!     E: Problem syncing the file - sync (5: Input/output error)     E: The package lists or status file could not be parsed or opened. Community user "stealing" tags? Using single quote by curly braces in String.format in Dynamic SOQL I'm struggling to use String.format to replace a token with a value when the token is within single quotes:  Example:  String query = String.format('SELECT Id FROM Availability WHERE Person__c = \'{0}\'', personId);   String query is equal to:  SELECT Id FROM Availability WHERE Person__c = {0}   Rather than:  SELECT Id FROM Availability WHERE Person__c = '234567890' "error: XDG_RUNTIME_DIR not set in the environment." when attempting to run nautilus as root I am attempting to run nautilus as root but when I run "sudo nautilus" from the terminal, I get the following error:     error: XDG_RUNTIME_DIR not set in the environment.      (nautilus:9341): Gtk-WARNING **: cannot open display:   The issue does not occur when I attempt to run nautilus as non-root. I am using ubuntu 14.04. Does anyone know how I can fix this? I have a dataset in csv file format that I'm loading into pgfplotstable. I can't change the format of the original csv, and being financial data it has a column of item names and two or three explanatory data points at the top of the table. e.g.  \documentclass{article} \usepackage{array,datatool,pgfplotstable}   \begin{filecontents}{sample.csv}     item,2008,2009,2010,2011      ,Actual,Actual,Forecast,Forecast      ,GBP,GBP,GBP,GBP      ,('000),('000),('000),('000) rounded     Area 1 OP, 1000000,1500000,1750000,250000     Area 2 OP, 400000,500000, 450000,-50000     Area 51 OP, 300000,375000,390000,15000     No P, 1250000, 1000000, 950000, 50000     Residuals, 800000, 80000, 90000, 10000   \end{filecontents}  \pgfplotstableread[col sep=comma]{sample.csv}\mystuff   I'm stumped at the next stage which is to typeset \mystuff so I have comma separators and can add a row that sums the 'Area' columns. At the moment to display the table I have to do something like  \begin{document}  \pgfplotstableread[col sep=comma,header=false]{sample.csv}\mystuff  \pgfplotstabletypeset[   columns/0/.style={string type},   columns/1/.style={string type},   columns/2/.style={string type},   columns/3/.style={string type},   columns/4/.style={string type}]\mystuff  \end{document}   How do I tag the top three rows as string and the rest of the last four columns as integer type so I can format and transform them? Restricing domains for universal and existential quantifiers I am currently using Rosen's "Discrete Mathematics and Its Applications" (7th ed.) for my discrete mathematics course. We recently talked about quantifiers, more specifically the universal and existential quantifier. What confuses me is when we started talking about restricting the domain (i.e. instead of all real numbers, only all real positive numbers), where does the conditional statement come from when restricting the domain of a universal quantifier and where does the conjunction come from when restricting the domain of a existential quantifier?  This link did help:   However, the part that confuses here is how are the domains restricted in the answer given in the link above? When can we use 'much' in affirmative clauses? I found the below in  web-site:     We use much in questions and negative clauses to talk about degrees of something.      We don’t use much in affirmative clauses.   Also, it the same web-site, I found the following:     She runs much faster than he does.    also I noticed that some web-sites use much with affirmative clauses:     May we all be having this much fun and getting this much exercise when we're his age!    Is it Okey to use much in affirmative clauses? If yes, when can we use it? and what is the rules?  Update:  Here is another example on how often the word "much" is used  in informal style:     After much consideration I will NOT be performing at the Inauguration with my improv group Capitol Hill-arious What does "upgrade to 18.04" mean? I'm using Ubuntu 16.04 LTS on an Asus K53E laptop with 8 GB RAM. I check for updates to the software daily. If there are no updates, it asks me if I want to upgrade? What does upgrade exactly mean? Will my personal files still be there? Will it wipe EVERYTHING and give me a completely new installation of Ubuntu? Or will it allow me to keep my files and applications, and merely upgrade the OS?  When I upgrade my Mac or Windows machines, my personal files remain available after the upgrade. Does Ubuntu do the same, or are there completely different "rules"? I would like to create a md5 checksum list for all files in a directory.  I want to cat filename | md5sum &gt; ouptput.txt. I want to do this in 1 step for all files in my directory.   Any assistance would be great. Google Chrome won't install on 17.04 I had to remove Chrome to have enough space to upgrade from 16.10 to 17.04.  I downloaded the latest version from Google.  But when it opens in the Ubuntu Software Manager, and I click on "Install", nothing happens. Hardy's Inequality for Integrals Is the collection of all functions between two sets a set? nginx httpMapModule regex variables The  states that:     Since 1.0.4, case insensitive regular expressions can be used by prefixing the pattern with ~*.   And gives the example:  map $uri $myvalue {     /aa                   /mapped_aa;     ~^/aa/(?&lt;suffix&gt;.*)$  $suffix; }   I updated to nginx/1.2.7 to make use of this, and naive regexes work okay, but variables don't. When I try the above syntax I get the error:  nginx: [emerg] pcre_compile() failed: unrecognized character after (?&lt; in "^/aa/(?&lt;suffix&gt;.*)$" at "suffix&gt;.*)$"   I also tried the following syntaxes, but none of them worked:  ~^(.*)$  $1; ~^(.*)$  \1;   but neither of them worked either.  Does anyone know how to get variables to work in regular expressions in HttpMapModule? How do I combine/exclude multiple tags from a search? I want to search for several related tags at once. When I type multiple tag-names in the search box, only one gets selected and I have to sift through a horde of non-pertinent questions.   E.g. 1: I want to find all questions where 'java' AND 'netbeans' AND 'tomcat' all are defined per question.  E.g. 2: (this may be a bit much to hope for) I want to find all questions where 'java' AND 'netbeans' BUT_NOT 'tomcat' is defined.  Alternatively, is there a way to search through the previous search results?  Is this possible? PHP mail function doesn't complete sending of e-mail Who is the Lord, as referred to in the title? Frodo? Sauron? Someone else? Or is it more of an abstract title, not referring to a single person, like "He who wields the One Ring"? Is it possible to create an iron door which responds to levers on both sides Evaluating $\int \sqrt{1 + t^2} dt$? How do we solve (i.e. get the closed form of) $\int \sqrt{1 + t^2} dt$ ?   shows the closed form of it but not the steps in solving it.  I think I need some algebraic trick..   I thought of some hyperbolic functions and their derivatives and equalities:  If I make $ t = \sinh x$, then I can reduce the integral to  $$ \int \cosh ^2 x dx $$ though I'm not sure if this is valid. But from here, I cannot go on evaluating the integral... I wanted a simple environment for making lists of equations, so I made one that includes an equation and a split environment. The code won't compile and the error seems unrelated. The most pressing thing I noticed was the &quot;You can't use `\end' in internal vertical mode.&quot; The problem is definitely the split environment. Here is a MWE. \documentclass{article} \usepackage{amsmath}  \newenvironment{env}     {\begin{equation}\begin{split}}     {\end{split}\end{equation}}  \begin{document} \begin{env}     x \end{env} \end{document}  If I remove the split environment from env, everything compiles just fine. Additionally, If the following example compiles just fine. What is the problem then? \documentclass{article} \usepackage{amsmath}  \begin{document} \begin{equation} \begin{split}     x \end{split} \end{equation} \end{document}  Here is the LaTeX error upon running the MWE. math.tex|11 error| LaTeX Error: \begin{split} on input line 9 ended by \end{env}. math.tex|12 error| LaTeX Error: \begin{equation} on input line 9 ended by \end{document}. math.tex|12 error| Missing $ inserted. math.tex|12 error| Missing } inserted. math.tex|12 error| Missing } inserted. math.tex|12 error| Missing } inserted. math.tex|12 error| Missing \cr inserted. math.tex|12 error| Missing { inserted. math.tex|12 error| Missing { inserted. math.tex|12 error| Extra }, or forgotten $. math.tex|12 error| Missing $ inserted. math.tex|12 error| Missing } inserted. math.tex|12 error| You can't use `\end' in internal vertical mode. math.tex|12 error| LaTeX Error: \begin{equation} on input line 9 ended by \end{document}. math.tex|12 error| Missing } inserted. math.tex|12 error| Missing $ inserted. math.tex|12 error| Display math should end with $$. math.tex|| Emergency stop. math.tex|| ==&gt; Fatal error occurred, no output PDF file produced! USB configuration within Developer Options doesn't save