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Factorial identity $n!=1+(1-1/1!)n+(1-1/1!+1/2!)n(n-1)+\cdots$ Show that $\displaystyle{n!=1+\left(1-\frac1{1!}\right)n+\left(1-\frac1{1!}+\frac1{2!}\right)n(n-1)+\cdots}$. I can't figure out how this can be solved. I tried to use the binomial theorem but I couldn't prove it. Any help will be greatly appreciated. When initiating a battle it starts off in AR mode, but then warns me saying my phone's orientation is not detected. I am then forced to turn off AR mode. Has anybody experienced this? If so, what are the solutions?    Per comments, I am unsure this is a permissions issue. I have everything turned on. In IE 9 you can type in whatever number you want to get the perfect zoom but in Chrome all I see is the + and - in the drop menu.  How do I choose a custom zoom and set it as the default? Why multiple PTR records in DNS is not recommended? I   that using multiple PTR records in a DNS configuration is not recommended.   However, the reasons are often vague, or not so obvious, naming:    "it can cause problems",  "can trigger bugs in programs expecting a single answer" : it's the software's problem then, isn't it?! "can make DNS answer packet too large" : isn't this fixed with ?   Are these good reasons? Do you know of any other (good) reasons? All this kinda looks like a "legacy fear"... Press space to continue How do I stop a bash script until a user has pressed Space?  I would like to have the question in my script     Press space to continue or CTRL+C to exit   and then the script should stop and wait until Space is pressed. Chain-calling parent initialisers in python Wine pollutes "Open With" application list The dialog box in question here is the one you get with the context menu option "open with other applications". Wine seems to have inserted more than a dozen or so entries for each application I install, which makes it a pain to find the correct application:     What can I do to remove the duplicates?     Update: Neither of the two solutions really work. The bug is interesting, but the symptoms does not match my problem (I'm not having problem with uninstalling applications, but rather the things that are inserted after installing them), and with the other one, all references to the Wine application are removed, which actually makes the problem worse (although it may be an acceptable solution if nothing else can be found). So this is still an open question; any takers? How to show the number of domains the disk is split into is $1+ C_n^2 + C_n^4$? Assuming there are n points on a circle, then there are $C_n^2$ chords. If any three chords don't intersect in circle. How to show the circle will be divided into $1+ C_n^2 + C_n^4$ domains?  Picture below is a example of 5 points on circle. Deriving even odd function expressions What is the logic/thinking process behind deriving an expression for even and odd functions in terms of $f(x)$ and $f(-x)$?  I've been pondering about it for a few hours now, and I'm still not sure how one proceeds from the properties of even and odd functions to derive: $$\begin{align*} E(x) &amp;= \frac{f(x) + f(-x)}{2}\\ O(x) &amp;= \frac{f(x) - f(-x)}{2} \end{align*}$$ What is the logic and thought process from using the respective even and odd properties, $$\begin{align*} f(-x) &amp;= f(x)\\    f(-x) &amp;= -f(x) \end{align*}$$   to derive $E(x)$ and $O(x)$?    The best I get to is: For even: $f(x)-f(-x)=0$ and for odd: $f(x)+f(-x)=0$  Given the definition of $E(x)$ and $O(x)$, it makes a lot of sense (hindsight usually is) but starting from just the properties. Wow, I feel I'm missing something crucial. Addons: Only some .zips will install Why does $\tan^{-1}(1)+\tan^{-1}(2)+\tan^{-1}(3)=\pi$? Playing around on wolframalpha shows $\tan^{-1}(1)+\tan^{-1}(2)+\tan^{-1}(3)=\pi$. I know $\tan^{-1}(1)=\pi/4$, but how could you compute that $\tan^{-1}(2)+\tan^{-1}(3)=\frac{3}{4}\pi$ to get this result? How to visualize a value resulted from math node,or just to know it. I tried the way of scaling this value to the scene size and then pick the color and get the value but I want more effective way to do this. A gold reviewer badge? Where does the term $|\psi\rangle\langle\psi|$ come from while calculating the expectation value? Induction problem: "if the group has at least one player who is better than Messi, then all the members of the group are better than Messi" How to encrypt external devices using a cross-platform solution? How can I check for an empty/undefined/null string in JavaScript? I saw , but I didn't see a JavaScript specific example. Is there a simple string.Empty available in JavaScript, or is it just a case of checking for ""? The meaning of various equality symbols Difference between 'struct' and 'typedef struct' in C++? using System; using System.Security.Permissions; using Microsoft.SharePoint; using Microsoft.SharePoint.Security; using Microsoft.SharePoint.Utilities; using Microsoft.SharePoint.Workflow;  namespace Change_Title_Event.Change_Title {     /// &lt;summary&gt;     /// List Item Events     /// &lt;/summary&gt;     public class Change_Title : SPItemEventReceiver     {        /// &lt;summary&gt;        /// An item is being added.        /// &lt;/summary&gt;        public override void ItemAdding(SPItemEventProperties properties)        {            properties.AfterProperties["Title"] = "Kevin: Changed by event receiver at" + DateTime.Now.TimeOfDay.ToString();            base.ItemAdding(properties);        }       } }   Where simple example, which works perfect on my local Sharepoint 2010. It is sandboxed.  But when I package this solution, it do not work on Sharepoint Online. I does not give any Errors either.  I think I am doing something wrong, something simple, but I can't simply find anything on Google about it.  Here is another who asks on the MSDN forum, but gets a very wierd reply, that I do not understand.