Prove that the series $a_n = $ $2^n \over n!$ converges to 0.
Prove that $\lim \limits_{n \to \infty} \frac{x^n}{n!} = 0$, $x \in \Bbb R$.
How can I prevent my Wi-Fi connection from glitching? Occassionally my Wi-Fi goes into this weird state where the phone "thinks" I'm connected, but the connection simply doesn't work.  Apps still seem to think I have connectivity, though they can't actually connect to anything, and the status bar still shows that I'm connected to Wi-Fi.  Turning Wi-Fi off and back on resolves the issue, and this occurs on multiple networks.  It seems sort of like whatever service manages the Wi-Fi connection gets killed occasionally.  It usually happens when I've been playing a game (that doesn't access the Internet) for a while or if my phone's been sitting for a while; it never happens while I'm actively using the connection.  I have my Wi-Fi timeout set to "Never" and the normal timeout isn't the issue since my phone regularly lasts several hours without the Wi-Fi dying.  Sometimes it dies a couple times in a day, and recently I went a week or so without it happening.  How can I fix this or prevent the service from being killed (if that's indeed what's happening)?  Shouldn't that be a system process that never gets killed?  (Does Android ever kill system processes other than when they crash?)  Could it be related to TouchWiz?  I have an SGS Vibrant running 2.2 (Bionix NextGen v1, but this has occurred on multiple ROMs). What is the difference between encrypting something and hashing something?  in what situations would I want one or the other? Why are there no line numbers in the code listings? Would it make discussing code easier if you could simply refer to a particular line or range, or am I wrong? If $A,B,C$ are the angle of a triangle, then show that $\sin A+\sin B-\cos C\le \dfrac32$ I tried substituting $C=180^\circ-(A+B)$ and got stuck. I also tried using the formula $\sin A+\sin B=2\sin \frac{A+B}{2}\cos \frac{A-B}{2}$ without any progress. Please help! Script failing with "command not found: ^M" When I try to run the following script in zsh, via the command /bin/zsh ~/.set_color_scheme.sh I get the following error:  command not found: ^M   The script has u+x permissions and it used to work on another machine that also had zsh. Any clues why?   Note: This question is related to  (where I am trying to adapt the script for tcsh)  #!/bin/zsh # Contents of set_color_scheme.sh  export LS_COLORS=$( \ ( grep '\w' | grep -v '^#' | sed 's/#.\+//' | perl -lane 'printf "%s=%s:", shift @F, join ";", @F;' ) &lt;&lt;&lt; "  # HUMAN_FORMATTED_DATA # list one per line  # these are basic filesystem items no 00          # normal fi 00          # file di 01 34       # directory ln 00 36       # link pi 40 33       # pipe so 00 35       # bd 40 33 01 cd 40 33 01 or 01 05 37 41 mi 01 05 37 41 ex 00 91       # executable ow 01 34       # other writables   *.cmd 00 32 *.exe 00 32  # archive, compressed things etc *.gz  00 90 *.bz2 00 90 *.bz  00 90 *.tz  00 90 *.rpm 00 90 *.rar 00 90 *.zip 00 90 *.iso 00 90   *.cpio 00 31    # perl &amp; CODE *.c      33 *.h      33 *.sh     33 *.t      33 *.pm     33 *.pl     33 *.cgi    33 *.pod    33 *.PL     33 *.js     33 *.php    33 #*.xs  # strikethrough *.off 00 9 *.bak 00 9 *.old 00 9   # documents misc, html webstuff # really TEXT *.htm    94 *.html   94 *.txt    94 *.text   94 *.css    94   # MOVIE *.avi    96 *.wmv    96 *.mpeg   96 *.mpg    96 *.mov    96 *.AVI    96 *.WMV    96 *.mkv    96  # images &amp; pdf *.jpg    96 *.jpeg   96 *.png    96 *.xcf    96 *.JPG    96 *.gif    96 *.svg    96 *.eps 00 96 *.pdf 00 96 *.PDF 00 96 *.ps  00 96  *.ai  00 91 # adobe ill *.doc 00 91 # msword   # data, such as .db, .csv *.csv    95 *.dsv    95 *.db     95 *.sql    95 *.meta   95 # CONFS *.xml    95 *.yaml   95 *.yml    95 *.conf   95 # [a-z0-9]*rc ") St. Matthew's vs. St. Matthew How to mass rename files with ill-formed numbering? Notification for reviews shows way too many Since a , I see more than I should:    I see no reason to see 134 posts are awaiting review, when there is literally nothing I can do about them. I think it is a bug, because notification is meant as something that will make me act. When I know I usually can't, obviously I will start to ignore it.  If it's not a bug, please remove bug tag and explain how it is supposed to be useful, or how can I switch to only seeing notifications about things I can act on.  Note that apaprently there are no flags for me, neither. I see only stats, migrated, close, delete, there, as if there was no flags waiting:    If you expect us to click on it every few minutes  just to see personalized numbers next to queues, why don't you simply query for personalized numbers every few minutes and cache them for us? It should cost you similar, in database usage, and will save us a lot of clicking and frustration.  If all this number means is "there might be reviews, or not" or "for sure there are none"  it would be simpler just to hide "review" link in the second case. We don't need two links with the same function next to each other, thank you, one is enough, and meaningless numbers are only irritating. Ubuntu 17.10 Upgrade Broke VMWare Workstation 12.5 Hi after upgrading to Ubuntu 17.10, vmware is now not starting.    I get the message:    /usr/lib/vmware/bin/vmware-modconfig: Relink `/lib/x86_64-linux-gnu/libbsd.so.0' with `/lib/x86_64-linux-gnu/librt.so.1' for IFUNC symbol `clock_gettime'   I am aware that there are patches available and I am attempting to apply these and recompile. I have run from the solution at :    cd ~   #Copy the vmmon source tar ball to your temporary location cp /usr/lib/vmware/modules/source/vmmon.tar .    #Extract the tar ball tar xf vmmon.tar    #Download the modified file that mkubecek posted and overwrite the one from the tar ball for VMware Workstation 12.5: wget -O ./vmmon-only/linux/hostif.c https://raw.githubusercontent.com/mkubecek/vmware-host-modules/b50848c985f1a6c0a341187346d77f0119d0a835/vmmon-only/linux/hostif.c     #Wrap up the newly modified files into a tar ball replacing the original one sudo tar cf /usr/lib/vmware/modules/source/vmmon.tar vmmon-only    #Rebuild the VMware kernel modules sudo vmware-modconfig --console --install-all   Failed to get gcc information.  gcc --version gcc (Ubuntu 7.2.0-8ubuntu3) 7.2.0 ...   Unforunately, vmware-modconfig is failing because of a dependency it seems on a particular gcc version. Am I on the right track? Any help with this issue would be much appreciated.  EDIT Thank you Steve, the below has gotten vmware going again. I've included minor correction. Tested and confirmed I could run a virtual machine.   sudo su    # do all below as root cd /usr/lib/vmware/modules/source tar xvf vmmon.tar  tar xvf vmnet.tar wget -O ./vmmon-only/linux/hostif.c https://raw.githubusercontent.com/mkubecek/vmware-host-modules/b50848c985f1a6c0a341187346d77f0119d0a835/vmmon-only/linux/hostif.c vim vmnet-only/bridge.c cd vmmon-only/ make cd ../vmnet-only/ make cd .. mkdir /lib/modules/4.13.0-16-generic/misc cp *.o /lib/modules/4.13.0-16-generic/misc insmod /lib/modules/4.13.0-16-generic/misc/vmmon.o insmod /lib/modules/4.13.0-16-generic/misc/vmnet.o rm /usr/lib/vmware/lib/libz.so.1/libz.so.1 ln -s /lib/x86_64-linux-gnu/libz.so.1 /usr/lib/vmware/lib/libz.so.1/libz.so.1 vmware-networks --start exit  # run vmware as normal user /usr/lib/vmware/bin/vmware Permissible for display name to advertise another SE site? Is it permissible to use your SE display name to advertise another SE site or Area 51 Proposal? Is this scrupulous or laudable?   I don't refer to my comment box. For example, could I change 'LePressentiment' to 'Commit to Law SE' to advertise the  proposal? Suppose that $\hat{x}$ is the least squares solution of $Ax = b$.  That is, $\min{|r|}, r = Ax - b$ with respect to $x$.  Is $\hat{x}$ also the least squares solution of $JAx = Jb$?  I suspect so, but I'm not sure how to prove it.  If $J$ is invertible, it's easy enough to prove as you can just cancel it out from both sides.  But what if it's not invertible? Let $f : \mathbb R^n \rightarrow \mathbb R$ be a measurable function.  We know that $f$ is not necessarily locally integrable - but how hard can a measurable $f$ fail to be so? For example, is it true that $f$ is locally integrable outside of a negligible set $N \subset \mathbb R^n$?   Edit: In consideration of the comment by zhs, let me correct the phrasing of the question. I was originally wondering whether the 'singular' behaviour of a measurable function can be localized to a 'small' set.   A motivational example is $f(x) = 1/x$ over the real line. It is locally integrable in the complement of the origin. Hence, a conceivable phenomenon, which I had in mind originally when asking the question, could be that a measurable $f$ is integrable over open sets that are compactly contained in the complement of some negligible sets. How can I confirm that my I-94 form was correctly processed after leaving the US in 2007? I've got a 32-bit Ubuntu installation running on 64-bit hardware. Now that , I would like to switch to 64-bit without having to reinstall the OS.  This is one of the :  Shawn installed his system using the 32-bit version of Ubuntu, but his hardware is 64-bit and he wants to switch over. He manually installs the amd64 versions of dpkg and apt, replacing the i386 versions and changing which architecture is used as the default; then he installs the amd64 ubuntu-minimal package; then he installs the amd64 ubuntu-desktop package. Over time the remaining i386 packages are replaced automatically on upgrade.  However, when trying to follow the instructions in there, I cannot find any 64-bit version of dpkg or apt.  Did this user story got implemented in a different way in the final spec, or do I need to do something differently?  In short, how can I switch my 32-bit installation to 64-bit? Check out the below program.   try {     for (String data : Files.readAllLines(Paths.get("D:/sample.txt"))){         String[] de = data.split(";");         System.out.println("Length = " + de.length);     } } catch (IOException e) {     e.printStackTrace(); }   Sample.txt:   1;2;3;4 A;B;; a;b;c;   Output:   Length = 4 Length = 2 Length = 3   Why second and third output is giving 2 and 3 instead of 4. In sample.txt file, condition  for 2nd and 3rd line is should give newline(\n or enter) immediately after giving delimiter for the third field. Can anyone help me how to get length as 4 for 2nd and 3rd line without changing the condition of the sample.txt file and how to print the values of de[2] (throws  ArrayIndexOutOfBoundsException)? Typing at symbol (shift+2) displays double quote (") and Typing at symbol (shift+') attherate (@) in ubuntu 16.04 I am working with ubuntu16.04. While working with terminal i had seen that my keyboard keys typing different signs. For example   Typing at symbol (shift+2) displays double quote (")  Typing at symbol (shift+') atTheRate (@)  Typing at symbol (shift+3) Euro (£)   .  I restarted my system but still it's showing same. Prove $x^3 + 3 =4y(y+1)$ has no integer solutions Each Stack Exchange site should provide users the option of using a dark mode design/theme.  Why is this feature missing?  The major IDEs are already a letdown regarding dark color schemes. How to use an alpha map in Blender Render? Which close reason should I use for questions that do not demonstrate research effort? I regularily encounter questions on StackOverflow which are asked only because of the sole fact that the poster haven't made the effort to google for and the docs of a particular function/class/framework/whatever. My question is, to which category of the five proposed one should I vote when I vote to close the question? Is it: off-topic, not constructive, not a real question, exact dupe or too localized? I tend to be all for 'not a real question' - am I quite right?