Proof of $\frac{x^n - a^n}{x-a} = x^{n-1} + x^{n-2}a + x^{n-3}a^3+...+xa^{n-2} + a^{n-1}$
Value of $\frac{x^n -a^n}{ x-a}$?
Random number generator only generating one random number Rootspaces are $\mathop{ad}$ nilpotent Rule of thumb for choosing an implementation of a Java Collection? Anyone have a good rule of thumb for choosing between different implementations of Java Collection interfaces like List, Map, or Set?  For example, generally why or in what cases would I prefer to use a Vector or an ArrayList, a Hashtable or a HashMap? I looked at similar questions and wanted to post a more specific one.  If I wanted one of my accounts on the network to no longer be associated to my global account, could an administrator do it manually? I mean, even if they could, would they?  It's a matter of professionalism. I don't want one of my accounts on the network to be visible from my other accounts. I just want that to be under a separate email that's not one of the OpenIDs associated with my global account.  I realize this would have been easier to do when I joined that site, but it's too late now, and only now have I realized that I don't really want that account showing up.  So can it be done by an administrator? I don't want to wait weeks and weeks for a response by using the contact form (funny, I've waited two with this post)... Suppose you cut a five year old's hair, save it for 10 years, and then use it for a Polyjuice transformation. What age do you turn into: The toddler or the teenager? What is Interface method in salesforce transforming ordinary generating function into exponential generating function I try to launch Firefox over SSH, using  ssh -X user@hostname   and then  firefox -no-remote   but it's very very slow.  How can I fix this? Is it a connection problem? Prove the map has a fixed point Assume $K$ is a compact metric space with metric $\rho$ and $A$ is a map from $K$ to $K$ such that $\rho (Ax,Ay) &lt; \rho(x,y)$ for $x\neq y$. Prove A have a unique fixed point in $K$.  The uniqueness is easy. My problem is to show that there a exist fixed point. $K$ is compact, so every sequence has convergent subsequence. Construct a sequence ${x_n}$ by $x_{n+1}=Ax_{n}$,$\{x_n\}$ has a convergent subsequence $\{ x_{n_k}\}$, but how to show there is a fixed point using $\rho (Ax,Ay) &lt; \rho(x,y)$? Proving that if $G$ has a Hamiltonian circuit, then the line graph $L(G)$ also has a Hamiltonian Circuit I have a graph G = (V, E). I know that the line graph L(G) of G is defined as follows: each vertex in L(G) corresponds to an edge in G, and two vertices are connected by an edge in L(G) if and only if the corresponding edges in G are adjacent.  Now I am trying to (a) prove that if G has a Hamiltonian circuit, then L(G) also has a Hamiltonian circuit, and (b) give an example of a graph G such that G does not have a Hamiltonian circuit but L(G) does.  However, I'm extremely stuck on how to do this, and any help would be greatly appreciated. Thanks so much! $\sum_{n=-\infty}^{\infty}\frac{1}{(n+\alpha)^2}=\frac{\pi^2}{(\sin \pi \alpha)^2}$? Precedence of user and group owner in file permissions I just ran into something unexpected (for me) regarding file permissions on Linux (Arch Linux). Basically I have:   userX in groupX fileX userX:groupX ---rwx----   What puzzles me: I cannot perform any action (rwx) on fileX. Is this right? Can someone please confirm this is indeed the expected behaviour?  The only actions I can perform are mv and rm because I have write permissions on the parent directory.  The thing is, I always thought these permissions collapse on each other, starting with the most general one (other -> group -> user). In other words, if o=rwx who cares what the persmissions for group and user are? Apparently this is not the case but it doesn't make much sense to me; it seems counterintuitive. The only thing this approach seems to be useful at, is to easily exclude a very specific person / group, which doesn't seem like a smart way to go at it (imho). Besides, the owner (and group?) should be able to chmod anyway right? Any thoughts on this matter? Is it possible to flash a smartphone like the Samsung Galaxy SIII or an LG Optimus 4X with a vanilla Android ROM like the one that has been flashed on Galaxy Nexus or Motorola phones (I think)?  I am asking because manufacturers like Samsung, LG, HTC tend to make ROMs for their smartphones and tablets with preinstalled launchers like Touchwiz or HTC Sense. They explain their decision by saying that they want to make their devices to look unique against their rival devices. The problem is that Android updates for their phones and tablets get delayed and there are incidents in which some devices - which are more than capable of running the upcoming version of Android - fall way behind or never get updated at all.   So, what I am basically asking here is if there is a way to install vanilla Android, excluding CyanogenMod or any other modified vanilla ROMs, on an Android based smartphone? My online friend is asking for money in order to visit my home country. Is this a legit request or a scam? On Travel.SE we often see questions about a person (usually a love interest) asking for money to pay for airfare, visas, permits and other expenses. For example        What general advice can be given in such situations to the person asking the question? Is it all a scam or can there be legitimate situations in which an online friend could be asking for money? Is a particular sequence required for detailed replicator requests?    To elaborate, is there a reason Captain Picard orders his tea, "Tea. Earl Grey. Hot." aka "Noun. Descriptor. Descriptor." and not "Descriptor. Descriptor. Noun." or "Descriptor. Noun. Descriptor." (in the event he forgot a descriptor)?  Would ordering it as "Hot. Earl Grey. Tea." or even the non-statement "Hot Earl Grey tea." produce a warm (hot), smoky (gray-ish) gas with the odor of tea?  I assume his ordering sequence is an acquired background affectation, but I'd like confirmation.  Note: I'm using "descriptor" instead of "adjective" to avoid minutia/debate about classification. JSON encode MySQL results How do I use the json_encode() function with MySQL query results? Do I need to iterate through the rows or can I just apply it to the entire results object? Writing test code for wrapper class I created a controller which looks like this  public with sharing class EventRegistrationController {      // A CONTROLLER FUNCTION     // FUNCTION RETURNS A LIST OF cSession      public List&lt;cSession&gt; getSessions() {            //DO STUFF       }     //A PUBLIC CLASS WITHIN CONTROLLER    @TestVisible public class cSession      {         public Session__c con {get; set;}         public Boolean selected {get; set;}          //This is the contructor method.          public cSession(Session__c c) {              con = c;             selected = false;         }     }  }   I need to write a test code for the controller, how can I create a list of cSession and call getSession function? Execute a large SQL script (with GO commands) I'm on a Toshiba Satellite C660_EL trying to install .   lspci -v Network controller: Realtek Semiconductor Co., Ltd. RTL8188CE 802.11b/g/n WiFi Adapter (rev 01)   However, I can't get the driver from there to compile (I've installed build-essentials already). Running make (with or without sudo makes no difference) I get  make -C /lib/modules/3.8.0-19-generic/build M=/root/rtl_driver modules make[1]: Entering directory `/usr/src/linux-headers-3.8.0-19-generic'   CC [M]  /root/rtl_driver/base.o In file included from /root/rtl_driver/base.c:39:0: /root/rtl_driver/pci.h:247:15: error: expected ‘=’, ‘,’, ‘;’, ‘asm’ or ‘__attribute__’ before ‘rtl_pci_probe’ make[2]: *** [/root/rtl_driver/base.o] Error 1 make[1]: *** [_module_/root/rtl_driver] Error 2 make[1]: Leaving directory `/usr/src/linux-headers-3.8.0-19-generic' make: *** [all] Error 2   There is a relevant PPA here:  but there's no 13.04 build.   Thanks in advance for any help! Objects Not Showing in Other Workspace Viewports, Only Default