I read that $e = \sum_{i=0}^\infty$$ 1\over n!$. This isn't immediately obvious to me, and I can't find proof of this. Can somebody explain to me, how do I prove this from definition $e = \lim_{n\to \infty}$$ (1 + {1\over n})^n $, or point me to one?
I guess the proof of the identity $$ \sum_{n = 0}^{\infty} \frac{1}{n!} \equiv \lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x $$ explains the connection between such different calculations. How is it done?
Let $d=GCD(n^2+5,n^3-5n^2+6n)$ show that $d|630$ I have a filename in a format like:     system-source-yyyymmdd.dat   I'd like to be able to parse out the different bits of the filename using the "-" as a delimiter. I've got a bunch of files named with a the pattern 99 - DescriptiveName.txt and I'd like to remove the number from the front so I just have DescriptiveName.txt.  How can I do this? Can I do it from the command line or is there a utility that can do this? One of the pertinent questions about many body systems that causes me much wonder is why the solar system is so stable for billions of years. I came across the idea of "resonance" and albeit an useful concept, it hardly explains the long stability of the solar system. Normally an N body problem with inverse square mutual interaction is an example of a chaotic system. Is there any real progress about this stability issue? Assign z values to depth curves in QGIS I'm new to QGIS and working with GIS in general (student of architecture), so please bear with me.  I have obtained shapefiles with topographic curves of an ocean floor. My intention is to export these as CAD files and render as 3D models of the ocean floor in Revit. I have done this procedure earlier with terrain shapefiles. My problem now is that these files mapping depth does not contain z values, so when exporting them into CAD they are completely flat rather than 3D models.  The depth information in meter exists as attributes in the file (see attached image). What I want is to transform this depth value into real z coordinates for each line so that the curves have different heights when importing as CAD file in Revit.  Thankful for any pointers in the right direction. I'm trying to write a blog post which includes a code segment inside a &lt;pre&gt; tag. The code segment includes a generic type and uses &lt;&gt; to define that type. This is what the segment looks like:  &lt;pre&gt;     PrimeCalc calc = new PrimeCalc();     Func&lt;int, int&gt; del = calc.GetNextPrime; &lt;/pre&gt;   The resulting HTML removes the &lt;&gt; and ends up like this:  PrimeCalc calc = new PrimeCalc(); Func del = calc.GetNextPrime;   How do I escape the &lt;&gt; so they show up in the HTML? Unicode Processing in C++ What is the best practice of Unicode processing in C++? Symbolic Link: Creating link from "NTFS Partiton" to ~/Desktop "Recent Badges" list is displayed without margins on "Home" page When the &quot;Hide Hot Network Questions&quot; preference is enabled (i.e. HNQ sidebar is hidden), we see &quot;Recent Tags&quot; and &quot;Recent Badges&quot; in the homepage instead of the HNQ. However, the &quot;Recent Badges&quot; list is displayed with no margins. ex.)   I think that the appropriate margins were set in the past. cf.) Probability expected value football problem The number of injuries at a college football game has the following probability distribution:      $$\begin{array}{|l:l|} \hline \textrm{Number of injuries} &amp; 0 &amp; 1 &amp; 2 &amp; 3 &amp; 4 &amp; 5 \\ \hdashline \textrm{Probability} &amp; 0.14 &amp; 0.33 &amp; 0.23 &amp; 0.17 &amp; 0.09 &amp; 0.04 \\ \hline \end{array}$$      The coach must file a report whenever there is more than one injury in any game.      a. Calculate the expected number of reports filed in the next 20 games.      b. Calculate the standard deviation of the number of reports filed in the next 20 games.      c. Calculate the expected number of football games to be played before the first game in which there are at least four injuries. Cannot access to (or find out) main Settings program Passing Account ID to my Visualforce Page As the user goes into an account, there is a custom button that they can click that will redirect them to my Visualforce page.  How can I capture that account id  in my controller?  Thanks  public myControllerCBR(){     breachRecord = new List&lt;wrapperClass&gt;();      AccountTeamMember uId = [SELECT UserId FROM AccountTeamMember WHERE AccountId =:ApexPages.CurrentPage().GetParameters().Get('id') and TeamMemberRole = 'Sales Engineer' limit 1];      List&lt;User&gt; uName = [SELECT Name, Manager__c, MANAGERID, Email, MOBILEPHONE FROM User WHERE Id =:uId.UserId limit 1];       for(User rept : uName){         breachRecord.add(new wrapperClass(rept));     }  }   See button setup: Permission denied in 777 folder john@ubuntu01:~$ sudo ls -l /var/opt/gitlab/git-data/repositories/GL/www.git total 25068 drwxr-xr-x  2 git  git      4096 aug 14 19:58 branches -rw-r--r--  1 git  git        66 aug 14 19:58 config drwxrwxrwx  2 root root     4096 aug 15 14:56 custom_hooks -rw-r--r--  1 git  git        73 aug 14 19:58 description -rw-r--r--  1 git  git        23 aug 14 19:58 HEAD lrwxrwxrwx  1 git  git        47 aug 14 19:58 hooks -&gt; /opt/gitlab/embedded/service/gitlab-shell/hooks drwxr-xr-x  2 git  git      4096 aug 14 19:58 hooks.old.1471193907 -rw-r--r--  1 git  git      1329 aug 15 14:48 index drwxr-xr-x  2 git  git      4096 aug 15 13:58 info drwxr-xr-x 71 git  git      4096 aug 15 14:55 objects -rw-r--r--  1 git  git        98 aug 15 13:58 packed-refs -rw-r--r--  1 git  git  25618530 aug 15 14:03 post-receive.log drwxr-xr-x  5 git  git      4096 aug 14 20:31 refs john@ubuntu01:~$ ls -l /var/opt/gitlab/git-data/repositories/GL/www.git ls: cannot access '/var/opt/gitlab/git-data/repositories/GL/www.git': Permission denied   Here are ACLs  john@ubuntu01:~$ sudo lsattr /var/opt/gitlab/git-data/repositories/GL/www.git/custom_hooks -------------e-- /var/opt/gitlab/git-data/repositories/GL/www.git/custom_hooks/post-receive   I have never seen this before. No permission to LS even with 777? I need to share this folder for more convenient development. How can I solve it? Thank you.  EDITED: (here are your requests)  john@ubuntu01:~$ sudo ls -ld /var/opt/gitlab/git-data/repositories/GL/www.git drwxrwxrwx 8 git git 4096 aug 15 14:48 /var/opt/gitlab/git-data/repositories/GL/www.git john@ubuntu01:~$ sudo ls -ld /var/opt/gitlab/git-data/repositories/GL/www.git/custom_hooks drwxrwxrwx 2 root root 4096 aug 15 14:56 /var/opt/gitlab/git-data/repositories/GL/www.git/custom_hooks   EDITED MORE  sudo ls -ld /var/opt/gitlab/git-‌​data/repositories/GL/‌​www.git ls: cannot access '/var/opt/gitlab/git-‌​data/repositories/GL/‌​www.git': No such file or directory   hmmm... what is this? Setting "checked" for a checkbox with jQuery I'd like to do something like this to tick a checkbox using jQuery:  $(".myCheckBox").checked(true);   or  $(".myCheckBox").selected(true);   Does such a thing exist? How can I get the Ubuntu shell on Windows 10 to recognize a connected android device? I'm trying to connect adb to my Android device in the Windows 10 Ubuntu shell, but it doesn't seem to be working:    adb does work normally on Windows, so it's not a problem with the phone or the connection.  Do I have to do something like mount the port in the Ubuntu shell?  How?  (The goal is to pass logcat to grep, which would obviously work better in Ubuntu.) When I double-click on a script in Nautilus to run it, the script just opens in my text editor with no option to run it. Using Nautilus, how do I run executable text files and/or scripts? Does a car use friction to move? Story with multiple 'third planet' races I'm looking for the name and author of a novel (or possibly novella). I first read this in the seventies, and might be older than that. It might have been written for teenagers.  The story takes place on a planet inhabited by a primitive humanoid race, roughly stone age if I remember rightly. Visiting this planet is a small team from a more advanced race, also humanoid and with spacefaring technology (obviously!). They are either there to help or observe, no nefarious purposes. I think they are avoiding contact with the primitives, at least initially. It's explicitly mentioned that the planet they are visiting is the third one of a medium sized star, just like their own homeworld. Also orbiting round the planet is an even more advanced race, using high tech to remain hidden from both the others. They are observing the whole situation, and again its mentioned that this is a 'third planet', like their own homeworld.  I'm a little bit hazy on the rest of the plot, but I think the super-advanced race end up revealing themselves, even though they are not supposed to.  The story is told from the viewpoints of both the second and third races (maybe also the first, I forget)  EDIT: For the record it turns out my recollection was faulty, and the second race are indeed coming to the planet for nefarious purposes. And the planet is at the medieval stage, not stone age. Can druids Wild Shape into creatures other than beasts? Under Wild Shape it says "assume the shape of a beast" you have seen before. Does this mean they can only transform into creatures that have the beast type, such as bear, wolf, crocodile, etc.? Or can they turn into things with other types, like dragon, monstrosity, humanoid, fiend, etc.? How do you send a HEAD HTTP request in Python 2? What I'm trying to do here is get the headers of a given URL so I can determine the MIME type. I want to be able to see if http://somedomain/foo/ will return an HTML document or a JPEG image for example. Thus, I need to figure out how to send a HEAD request so that I can read the MIME type without having to download the content. Does anyone know of an easy way of doing this?