How can I evaulate the following series?  $$\sum_{k=1}^{n} 2^{k}k$$  I don't know where to begin. $2^k$ alone would be straight forward.
How can I evaluate $$\sum_{n=1}^\infty\frac{2n}{3^{n+1}}$$? I know the answer thanks to , but I'm more concerned with how I can derive that answer. It cites tests to prove that it is convergent, but my class has never learned these before. So I feel that there must be a simpler method.  In general, how can I evaluate $$\sum_{n=0}^\infty (n+1)x^n?$$
Textarea CSS issue on "needs moderator attention" To reproduce:   Click Flag (question or answer) Click other (needs moderator attention)   The textarea is too wide:  StackOverflow        AskUbuntu        StackExchange        Most probably affects other sites, but didn't check. I think it's enough. :-)  Reproducing on:   Chromium Version 40.0.2214.111 Ubuntu 15.04 (64-bit) Google Chrome Version 41.0.2272.76 (64-bit) Firefox 36.0   (I'm using Ubuntu 15.04) Creating your own Tinyurl style uid Make \cite{my reference} show name and year I am trying to figure out how to make author's name and year show up every time I make a reference.  For example:  my_bibtex.bib has this entry:  @article{Franklin1999,  author = {Franklin Allen and Risto Karjalainen}, title = {Using genetic algorithms to find technical trading rules}, year = {1999}, volume = {51}, pages = {245-271}, journal = {Journal of Financial Economics}  }   If in my_paper.tex I use this line:  Important result has been found by \cite{Franklin1999}   My output looks like:  Important result has been found by [1]   But I want it too look like:  Important result has been found by Franklin 1999   I there a way to do it?  My bibliographystyle is set to plain  \bibliographystyle{plain}  \bibliography{my_bibtex} Returning from a finally block in Java I was surprised recently to find that it's possible to have a return statement in a finally block in Java.  It seems like lots of people think it's a bad thing to do as described in ''. Scratching a little deeper, I also found '' which shows some pretty horrible examples of other types of flow control in finally blocks.  So, my question is, can anyone give me an example where a return statement (or other flow control) in a finally block produces better / more readable code? Tabs in output file written by xelatex and pdflatex are different Is an HTTPS query string secure? I am creating a secure web based API that uses HTTPS; however, if I allow the users to configure it (include sending password) using a query string will this also be secure or should I force it to be done via a POST? Upper bound on $\chi(G)$ for a triangle-free graph I'm struggling with the following question;     For every graph $G$ such that $K_3 \not\subseteq G$ (i.e. $G$ does not contain a triangle), prove that $\chi(G) \leq 2\sqrt{n} +1$ (where $\chi(G)$ denotes the chromatic number).   Any hints? I really cannot see the connection between the triangle-free nature of $G$ and a chromatic number being bounded above by $O(\sqrt{n})$. After Windows 10 Fall Creators Update, a svchost.exe instance is constantly using CPU time Since installing the Windows 10 Fall Creators Update, I have a svchost.exe process that is constantly using about 14​ % of CPU time:    This svchost.exe instance is responsible for hosting three services:    The CPU time is consumed by a thread inside that process that  cannot attribute to any of these three services:    Given that these three services are considered critical system services, it's hard to do anything about them. These services cannot be stopped or disabled by services.msc, and terminating the process triggers a bugcheck (CRITICAL_PROCESS_DIED). Disabling the Windows Defender Firewall through the settings UI does not reduce CPU usage.  I'm out of ideas. What could be causing this? How can I debug this further? Is there a workaround to stop these services?    Update: After some debugging with , we've isolated this to the Windows Defender Firewall service. Process Monitor shows that it's constantly accessing the registry:    A CSV export of a Process Monitor capture, filtered to that process, is available .  I’m still looking for a way to stop that behavior.    Update 2: Analysis with the Windows Performance Analyzer shows that most CPU time is consumed by code from rpcrt4.dll: Heat production of magnifying glass Why Magnifying glass(convex lens) produces heat when placed in front of sun? Missing $ inserted Forgive my ignorance. The below seems 'inconsistent'. If canceling the $(x+1)$ is 'legal', how does the domain change? I realize it does, but would someone be so kind as to provide an explanation?    $$ \frac{x^2 - 1}{x + 1} \mbox{ is undefined when } x = -1 $$  Its domain (the values that can go into the expression) does not include $ -1 $.  Now, we can factor $ x^2 - 1 $ into $ (x - 1)(x + 1) $ so we get:  $$ \frac{(x - 1)(x + 1)}{(x + 1)} $$  It is now tempting to cancel $ (x + 1) $ from top and bottom to produce:  $$ x - 1 $$  $$ \mbox{Its domain now } \textbf{does} \mbox{ include } -1 \mbox{.} $$  But it is now a different function because it has a different domain.    Thanks! Explanation of method for showing that $\frac{0}{0}$ is undefined (This was asked due to the comments and downvotes on this  answer. I am not that good at maths, so was wondering if I had made any basic mistakes)  Ignoring limits, I would like to know if this is a valid explanation for why $\frac00$ is undefined:     $x = \frac00$    $x \cdot 0 = 0$        Hence There are an infinite number of values for $x$ as anything multiplied by $0$ is $0$.   However, it seems to have got comments, with two general themes.  Once is that you lose the values of $x$ by multiplying by $0$.  The other is that the last line is:      $x \cdot 0 = \frac00 \cdot 0$   as it involves a division by $0$.  Is there any merit to either argument? More to the point, are there any major flaws in my explanation and is there a better way of showing why $\frac00$ is undefined? Cancellation Law for Direct Sums - What is wrong with this argument? Underscores in custom fields While trying to perform a WP_Query using meta_query(), I had some trouble because the custom fields created by a plugin had _ in the beginning of its name.   Although I noticed it was stored this way in the database, I had no idea why it was there and thought I had to reference it without the underscore (for the record, that is wrong).  Why do some custom fields start with underscores and others don't? What are the underscores used for? Are they mandatory in some circumstances? Bash string range and replace To print part of the string, replace , with . I use command:  echo "${q:16:6}" | sed 's/,/./'   Is it possible to use something like:  echo "${q:16:6/,/.}"   because it does not work? Android Debugging, how? Proving a trig identity: $\frac{\sin(A + B)}{\sin(A - B)}=\frac{\tan A + \tan B}{\tan A - \tan B}$ A mathematically mature introduction to Turing Machines and Computability [reference-request] In the computer science course for mathematicians held at my university Turing Machines have been presented very briefly. So much so that I didn't quite get why they are relevant to mathematics. I did understand what a Turing Machine is, but I feel that the presentation given was (for schedule reasons) quite naive and simplified. So I would like to ask if you can point out a good reference for a mathematically mature introduction to turing machines and computability. Can we modify "Ask question" to automatically suggests tags based on your question content.   So instead that user needs to type "team-foundation-server" or "TFS" or "TeamFoundationServer" he will see list of tags auto-populated with ajax which he (or she) can then select and it will be associated with the question. So basically only thing we need is code which will cross-match question content with list of known tags while user is typing and display results in some nice ajax-enabled list/cloud/whatever UI control. This should be separate control for tags suggestions so user still has option to use standard tag list input to type-in tags.  In this case, instead of three (or more) tag variations we would have only one tag for Team-Foundation-Server. Help with packages in java - import does not work I'm a C++ developer - not a java developer, but have to get this code working...  I have 2 public classes that will be used by another product.  I used the package directive in each of the java files.    package com.company.thing;  class MyClass ...   When I try to compile a test app that uses that I add   import com.company.thing.*;   The javac compiler fails with errors about com.company does not exist.  (even if I compile it in the same directory as the class files I just made a package of)  I am sure I am doing something bone-headed and silly.  I've read the  pages and tried to set up a directory structure like /com/company/thing  etc, but either I have totally screwed it all up or am missing something else.  EDIT thanks for the suggestions - I had tried the classpath previously.  It does not help.  I tried compiling   javac -classpath &lt;parent&gt; client.java    and the result is:  package com.company does not exist   I have the code I want to import (the two java files) in \com\company\product.  I compile those fine.  (they contain MyClass) I even made a jar file for them.  I copied the jar file up to the parent directory.  I then did (in the parent directory with the client java file)   javac -cp &lt;jarfile&gt; *.java   the result is:  cannot access MyClass bad class file: MyClass.class(:MyClass.class) class file contains wrong class: com.company.product.MyClass Please remove or make sure it appears in the correct subdirectory of the classpath.   EDIT  I got the client code to compile and run if I used the fully qualified name for MyClass and compiled it in the parent directory.  I am totally confused now.    compiled with no classpath set - just   javac *.java    in the parent directory - and it worked fine.  I can get a test app to compile, but that is not going to cut it when i have to integrate it into the production code.  Still looking for help.  EDIT:  Finally - not sure why it didn't work before - but I cleaned up all the files all over the directory structure and now it works.    Thanks