Limit exists or not? $\lim \limits_{n \to\infty}\ \left[n-\frac{n}{e}\left(1+\frac{1}{n}\right)^n\right] $
How do I find this limit: $\lim_{n\to\infty} \left[ n-{n\over e}\left(1+{1\over n}\right)^n \right]$?
Turn off close Facebook friend notification How can I make an X-Y scatter plot with histograms next to the X-Y axes? Does Change Data Capture (CDC) work in a SQL Server 2012 AlwaysOn Failover Cluster Instances setup? Does  work in a  setup?  There would be two nodes in the AlwaysOn Failover Cluster Instances setup and two Domain Controllers.  We are not using AlwaysOn Availability Groups.  Will CDC work? and will it failover? Can the Eclipse Java formatter be used stand-alone Is there a way to use the formatter that comes with eclipse, outside of eclipse?  I would like to format some java files using my formatter.xml file that I have configured using eclipse.  Does anyone have any code examples that would allow me to do this?  I would also like to use this standalone, so the specific jars that are used would be nice. Visual Studio C# statement collapsing When editing really long code blocks (which should definitely be refactored anyway, but that's beyond the scope of this question), I often long for the ability to collapse statement blocks like one can collapse function blocks.  That is to say, it would be great if the minus icon appeared on the code outline for everything enclosed in braces.  It seems to appear for functions, classes, regions, namespaces, usings, but not for conditional or iterative blocks.  It would be fantastic if I could collapse things like ifs, switches, foreaches, that kind of thing!  Googling into that a bit, I discovered that apparently C++ outlining in VS allows this but C# outlining in VS does not.  I don't really get why.  Even notepad++ will so these collapses if I select the C# formatting, so I don't get why Visual Studio doesn't.  Does anyone know of a VS2008 add-in that will enable this behavior?  Or some sort of hidden setting for it?  Edited to add: inserting regions is of course an option and it did already occur to me, but quite frankly, I shouldn't have to wrap things in a region that are already wrapped in braces... if I was going to edit the existing code, I would just refactor it to have better separation of concern anyway. ("wrapping" with new methods instead of regions ;) Dragon souls not activating new words So if I understand correctly you can learn new words and the souls will activate these words. I just killed a dragon and when it died it looked like I absorbed the soul but it didn't unlock any of the words I have.   I noticed some dragons actually have a name so do certain dragons unlock certain words? shred multiple hard drives Every finite subset of $\mathbb R$ contains its supremum (and its infimum)   Proof Let $A=\{a_1,...,a_n\}$ be a finite subset of $\mathbb{R}$. Since it is non-empty and it is bounded ($\max A$ is an upper bound), it has supremum, that is $\exists \sup A$ and by definition $\forall a \in A \;\, a \leq \sup A$. Let's suppose that $\sup A  \not\in A$ then, since $\max A \in A$ we have that $\max A &lt; \sup A$. But considering that $\mathbb Q$ is dense in $\mathbb R$ we can conclude that $\exists r \in \mathbb Q$ s.t. $\max A &lt; r &lt; \sup A$, but this is absurd since $r$ is an upper bound of $A$ and it is lower than the supremum. Necessarily, $\sup A\in A$.  Is there anything wrong? Is there any way to prove this without using density of $\mathbb Q$ or another property? Thanks in advance. Multiple entry visa to UK (sponsored visitor) What is the mysterious stranger doing in my vault? My local hackerspace has a CNC machine.  I can give them my Gerbers and they can print out the PCB.  The machine does not plate VIAs.  I need to do this after the CNC machine is finished.  What is the best process and materials to use? Can a familiar attune and wear or use a magic item? Is it possible for a familiar to attune to and then wear or wield a magic item? Invalid characters for XML parsing in posthistory.xml from Stack Overflow We got the April 2011 data dump from Stack Overflow and, while trying to put everything into a database, we got      SyntaxError: reference to invalid character number: line 1105549, column 5445   in the middle of the posthistory.xml file. It seems that there are sets of characters (&amp;#xC I believe) within a few posthistory entries which break our XML parser.  Is there a solution besides manually changing all the C's? Pretty tricky cmd Presently, how much information can a quantum computer store, in how many qubits? What restrictions are there and how does it vary across realizations (efficiency of data storage, ease of reading and writing, etc)? How do I set up a shipping condition that accesses the value of a specific field in product? I have a term reference field in product called "Weight" with values "Light", "Medium" &amp; "heavy". I am using flat rate shipping service and trying to check the value of "Weight" field in Calculation rules.I know that I need to expose it by using "entity has field" but I end up having  commerce-line-item:order:commerce-line-items:0 commerce-line-item:order:commerce-line-items:1 commerce-line-item:order:commerce-line-items:2 commerce-line-item:order:commerce-line-items:3 commerce-line-item:order:commerce-line-items:0... commerce-line-item:order:commerce-line-items:1... commerce-line-item:order:commerce-line-items:2... commerce-line-item:order:commerce-line-items:3...    I was able to get to the weight field by using any of them and then did a Data Comparison  commerce-line-item:order:commerce-line-items:0:commerce-product:field-product-weight   this condition worked ok first time but not after that. can anyone please help me on this or if you think of another solution please let me know. Thanks How do I find a recursion formula to solve the following question:  In how many sequences of length $n$, with elements from $\{{0,1,2,3,4}\}$, the difference between every 2 adjacent elements is $1$ or $-1$?  I've been trying to solve the problem for the last 5 hours maybe, I'm sure that I'm missing something..   This is a problem in combinatorics, and the solution must be by finding a recursion formula for the problem.   best solution I've come so far is that if we say that $a_n$ is the solution to the question, so let's count how many sequences of size $n-1$ there are that meet the requirement, and we complete the first element to make it a sequence of $n$ elements. so for $n-1$ there $a_{n-1}$ sequences, and for each sequence we have $2$ options to choose the first element (one option is to take a plus $1$ number from the number that start the $n-1$ sequence, and the other option to to take a minus $1$ number from the number that start the $n-1$ sequence), only problem as you figured out is that if the $n-1$ sequnce starts with $0$ or $4$ there is only $1$ option left for the first element in the sequnce.. so $a_n=2a_{n-1}$ won't work.  I think that the solution may involve using $2$ or maybe $3$ recursion formulas.  Hope I was clear enough. Proving an infinite number of primes of the form 6n+1 The proofs given on other sites weren't that clear and used different methods that I have yet to learn.    Prove that there are an infinite number of primes of the form 6n+1.  The hint that was given was: Let p = p1, p2, ..., pk + 1, where p1 = 2, p2 = 3,...pk are the first k primes.  Show that p is prime.  (p1 means p sub 1, p2 means p sub 2, and pk is p sub k.  Wasn't sure how to write it on this.)    Can someone explain this hint on how they came about of p1 = 2, p2=3, etc, and prove this please?    Also, how would the proof change if the form changed?  ("Prove that there are infinite number of primes of the form....") git-upload-pack: command not found, when cloning remote Git repo I have been using git to keep two copies of my project in sync, one is my local box, the other the test server. This is an issue which occurs when I log onto our remote development server using ssh;  git clone me@me.mydevbox.com:/home/chris/myproject Initialized empty Git repository in /tmp/myproject/.git/ Password: bash: git-upload-pack: command not found fatal: The remote end hung up unexpectedly fetch-pack from 'me@me.mydevbox.com:/home/chris/myproject' failed.   (the file-names have been changed to protect the guilty... !)   Both boxes run Solaris 10 AMD. I have done some digging,  if I add --upload-pack=$(which git-upload-pack) the command works, (and proves that $PATH contains the path to 'git-upload-pack' as per the RTFM solution)  but this is really annoying, plus 'git push' doesn't work, because I don't think there is a --unpack= option.    Incidentally, all the git commands work fine from my local box, it is the same version of the software (1.5.4.2), installed on the same NFS mount at /usr/local/bin.    Can anybody help? Citing two authors gets displayed incorrectly