What is the interpretation of this identity? I've tried picking elements one-by-one and grouping them, looking for geometric interpretations by drawing polygons and still no success.
I am attempting to solve this counting problem through combinatorial argument. The following is the equation I am given:   $$\sum_{i=1}^n (i-1)(n-i) = \binom{n}{3}$$  I understand that the right-hand side of this equation represents a set of $n$-elements out of which we choose 3. For example I believe we can say suppose we have a group of $n$ people and we want to choose 3 out of $n$ to be in a committee. However I'm not sure how to express the left-hand side in words. If forming a committee is an appropriate way to tackle this problem then I know the left-hand side must utilize the addition and multiplication principles, but I don't know how to put it into words. Also my intuition tells me that in solving this we should first flip $$(n-i)(i-1)$$  Thanks!
Are there other governments in The Hunger Games world? We know that Panem exists in a post-apocalyptic North America but are there other established governments on other continents? How do Android tablets use magnet to auto-lock the device? How to install LXDM instead of GDM3? I'm running Debian Wheezy and my default Display Manager is GDM3, and I would like to replace it with LXDM. The problem is that I'm trying to run # apt-get install lxde and it's not working, what am I doing wrong?  My /etc/apt/sources.list is:  deb cdrom:[Debian GNU/Linux testing _Wheezy_ - Official Snapshot i386 DVD Binar$  deb http://ftp.br.debian.org/debian wheezy main deb-src http://ftp.br.debian.org/debian/ wheezy main  deb http://security.debian.org/ wheezy/updates main contrib deb-src http://security.debian.org/ wheezy/updates main contrib How do I use RelativeSource with WPF bindings and what are the different use-cases? Flagged emails keep returning and won't synchronize between Apple Mail and Gmail I've had this problem before and can't recall how I managed to fix it last time. I use Apple Mail to access my Gmail and normally flagged emails show up correctly. Starred emails in Gmail equate to flagged emails in Apple Mail and I can unflag an email in either Gmail or Apple Mail and it works.  But now I've got four emails that I can't unflag. They're not flagged in Gmail at all (although they used to be). When I see them in the Flagged folder in Apple Mail, they don't even have flag icons next to them but they're still counted in the number showing next to "Flagged". If I manually re-flag them and then unflag them, they disappear from the Flagged box. But then if I click into Inbox and then back into Flagged they show up again.  Any ideas about how to make these guys disappear for good?! While I applaud the excellent work of , the question has come up:     How long will be the elected moderator’s “mandate”? Is it for life, or are we going to have “moderator elections” regularly?   Of course, any community moderator who wishes to recuse him or herself can certainly do that at any time.   Should we have term limits that require community moderators be cycled out periodically, so others get a chance to moderate? Should we hold regular (say, yearly) moderator elections? Is it better to have a larger pool of community moderators, and let the normal ebb and flow of turnover get us "natural" variability in moderation?   What are your thoughts on this? How do I add Headers in List of Tables page? I have a batch file which is in a directory and must be run from there as well because it updates files within this directory. This works perfectly fine, except when the user runs the batch file as administrator (required on Vista). Then the starting directory is C:\Windows\System32. Is there any way to still be able to know from which directory the batch file was run? I dont want the user to enter the directory manually. Localization of ideals at all primes says:  SSH_ASKPASS    If  ssh needs a passphrase, it will read the passphrase from the    current terminal if it was run from a terminal.  If ssh does not    have  a  terminal associated with it but DISPLAY and SSH_ASKPASS    are set, it will execute the program  specified  by  SSH_ASKPASS    and open an X11 window to read the passphrase.   I'd like SSH to use an askpass program even if it was run from a terminal.  On occasion, I have to connect to servers, where there's some delay in showing a password prompt (maybe due to network issues, maybe due to attempted reverse DNS lookups, …). I get annoyed and switch to something else, and forget about the attempted connection. (Insert joke about attention span of a goldfish.) When I finally get back to it, the prompt's timed out and even a correct password would just result in a closed connection.  Keys would be one solution, but not every system I use has my usual SSH keys. However, I usually use Ubuntu systems, and Ubuntu has an SSH askpass program installed by default.  If an askpass window popped up, however, I'd be immediately aware of it. That's a good enough compromise for me, if only I can get it to work. Why can I not access a file named `-` when quoting? I have a file called -.  I want to display its contents.  One way is to do  cat ./-   since cat - reads from standard input. However, why are cat "-" and cat '-' also interpreted by the shell as cat -? MATLAB/OCTAVE Extracting elements from different sized vectors in a cell array What are these notices above my post? My post has been marked with an informational notice in a box above it.   What should I do about this? Who attaches notices to posts? What kinds of notices are available? What should I do if I think a notice should be added to a post? What should I do if I think a notice should be removed from a post? Can Muggles publicly establish the existence of a magical community? Let $S = \{1,2,\dots,n\}$. Then $i \in S$ is said to be a fixed point of a permutation $p$ or $S$ if $p(i) = i$. Let $P_n(k) $ be the number of permutations of $S$ which have $k$ fixed point. Prove that $\sum_{k=0}^nk\cdot P_{n}(k) = n!$. Grub menu at boot time... "holding shift" not working I read here at  that holding Shift during boot can bring up the GRUB menu. However I try holding one or the other Shift keys, tapping, tapping then holding, nothing works. Am I missing something? How does one access the GRUB menu during boot time?   No dual boot here, just standard Lubuntu 14.04 install. Reference — frequently asked questions about PDO How to compare Unicode strings in Javascript? I have a custom search page for use in Customer Portal.  VF Page:    &lt;form name="frmSearch"&gt;      &lt;input type="text" name="keyword" id="keyword" value="{!portalSearchModel.searchTerm}" onkeypress="return noenter(event);" style="width:25%; height:25px;margin:0; padding: 0px 6px 0px;" placeholder="What are you looking for?" /&gt;      &lt;input type="button" id="btnSearch" name="btnSearch" value="Search" onclick="searchTerm()" class="go-we3" /&gt;   &lt;/form&gt;   &lt;script type='text/javascript'&gt;       function searchTerm(){         var searchTerm = document.getElementById("keyword").value;          var url="/apex/PortalSearch?s="+searchTerm;          window.location = url;          return false;     }          &lt;/script&gt;   Is there a way to call this apex method in Controller on button click along with the JavaScript?      public void logSearchTerm(){         portalSearchModel.searches();         Search_Log__c sl = new Search_Log__c();          sl.search_term__c = portalSearchModel.searchTerm;         sl.user__c = UserInfo.getUserId();              insert sl;  } Note: TL;DR, scroll to bottom for summary. I recently set up my computer for a dual boot between Ubuntu 9.10 and Windows 7. My current drive setup is as follows.  | A1 |     A2       | | B1    |  B2  | B3 |        A1: 100 mb, windows 7 "System   Reserved" boot partition      A2: 230 gb, data section, this one   needs to be shared between the   operating systems      B1: 125 gb, windows 7 OS      B2: 123 gb, ubuntu OS      B3: 2gb, linux swap space     Pretty much I want to have my documents, music, pictures, videos, etc accessible from both operating systems. My first attempt involved making the data (a2) partition NTFS, and moving my home folder from ubuntu to the data partition. However, as I read NTFS does not work nice with permission, and it messed up my home folder. My next idea is one of the following: 1) format the data partition to ext2/3/4 and move my home folder from linux there, and get a driver to read ext partitions in windows 7. The problem with that is that most of the ext drivers/software are not compatible with windows 7 or do not integrate with windows explorer (I really don't want to open a separate software window just to access my data, plus it's probably not compatible with other software.)  looks promising, but I'm not sure how it works with ext4 and windows 7 (not officially supported, when trying in Vista Compatibility Mode, it tells me I need to format the ext drive to use it). My next idea, 2) keep the home folder in ubuntu where it is, but create symlinks for the Documents, Music, etc folders to an NTFS formatted Data (A2) partition, and add those locations to the windows 7 libraries. I'm not totally sure how the permissions would work out, but it should be fine since it's only the documents, music, etc and not the important config files in the rest of /home/user/. Correct me if I'm wrong. Currently, symlinks is my best idea, although i'm not sure how it will work.  Any suggestions, additions to my ideas, links, pointers, whatever would be greatly appreciated. Even if it means I should reformat both my drives and repartition (2 250gb drives if you want to suggest a setup for that), I won't be too opposed if that's the best suggestion (I've gone through the format/install/format/reinstall process 5 times over the past 3 days, once more won't hurt me).    TL;DR, summary:  I have two hard drives. One is partitioned for Ubuntu and Windows 7, the second one I want accessible to both operating systems to store documents, music, pictures, videos, etc. Suggestions on how to set up the data drive.    P.S. bonus if I can get an apache server document root folder working between the two OS's as well (permissions could become very complicated, so don't worry too much about that)  P.P.S. Related question, but data viewing is one way: