Verify the identity $\sum_{k=0}^n \frac{(2n)!}{(k!)^2((n-k)!)^2} = \dbinom{2n}{n}^2 $
Vandermonde identity corollary $\sum_{v=0}^{n}\frac{(2n)!}{(v!)^2(n-v)!^2}={2n \choose n}^2$
What is rank deficiency, and how to deal with it? Evaluate $\lim_{x \to 0} (x\lfloor\frac{1}{x}\rfloor)$  I'm trying to solve it by using the squeeze theorem but I'm stuck.  I'm looking for a function $g(x)$ such that $g(x) \leq x\lfloor\frac{1}{x}\rfloor \leq x(\frac{1}{x}) = 1$  Can anybody give me a hint? Completely synchronise multiple Macs I generated a key and copied it to my target:  ssh-keygen ssh-copy-id username@hostname   I left the the location of the key as default and did not set any passphrase.  For a small while after that, I was able to ssh username@hostname without being prompted for a password, and then it stopped working for some reason. I'm writing a sports management simulation game. Like most sport management games, it makes heavy use of statistics. I would like to use real players, teams and league names.  i) Am I running the risk of getting into legal battles if I should use the real names? ii) Also what about team colours and emblems etc?    Update Much thanks for all the input! How do I remove hidden backup files? I have files ending in ~ in my home directory, and I want to delete them. How do I do that? How do I prevent this backup functionality? How do you sort du output by size? How do you sort du -sh /dir/* by size? I read one site that said use | sort -n but that's obviously not right. Here's an example that is wrong.  [~]# du -sh /var/* | sort -n 0       /var/mail 1.2M    /var/www 1.8M    /var/tmp 1.9G    /var/named 2.9M    /var/run 4.1G    /var/log 8.0K    /var/account 8.0K    /var/crash 8.0K    /var/cvs 8.0K    /var/games 8.0K    /var/local 8.0K    /var/nis 8.0K    /var/opt 8.0K    /var/preserve 8.0K    /var/racoon 12K     /var/aquota.user 12K     /var/portsentry 16K     /var/ftp 16K     /var/quota.user 20K     /var/yp 24K     /var/db 28K     /var/empty 32K     /var/lock 84K     /var/profiles 224M    /var/netenberg 235M    /var/cpanel 245M    /var/cache 620M    /var/lib 748K    /var/spool Sorry, I'm still a newbie to blender, but why are some edges visible only in edit mode, but not in wireframe view? is it a bug or am I missing something here?  edit mode: Edges visible. Object mode, wireframe view: Pooff, they're gone. what can i do to fix this? / thanks How do I move Steam games to a new computer without re-downloading them? I have just bought a new computer and I have everything migrated over except for my Steam games.  I looked in Program Files/Steam/ and I found a folder full of the games I have downloaded, but I do not know if it is safe to just copy these folders from one computer to another (seeing as a lot of other applications will not work if you do this), or is there another recommended way?  I don't really feel like re-downloading all my games. I don't have the time nor bandwidth to download 20GB over a 1.5mbps connection.  Is it possible to contact Valve and get a disk with the games on it? Create Task in loop but all tasks take the same parameter From Wikipedia :     Suppose you're on a game show, and   you're given the choice of three   doors: Behind one door is a car;   behind the others, goats. You pick a   door, say No. 1, and the host, who   knows what's behind the doors, opens   another door, say No. 3, which has a   goat. He then says to you, "Do you   want to pick door No. 2?" Is it to   your advantage to switch your choice?   The answer is, of course, yes - but it's incredibly un-inituitive. What misunderstanding do most people have about probability that leads to us scratching our heads -- or better put; what general rule can we take away from this puzzle to better train our intuition in the future? Font characters displayed as squares in Ubuntu 18.04 Recently, on my Ubuntu 18.04 I have noticed that at least on gnome-calculator and chromium browser the fonts are displayed as squares. I have followed instructions  and , the calculator is fixed, but the problem on chromium still exists when I open a dialog to search for a file.  Not sure if this happens on other applications as well, I haven't checked all my apps, but File managers nemo and nautilus are working fine.  Also, before few months ago, I have included some windows fonts for my libre office shown . I used the copy (cp) method, not the link (ln -s). But, was working fine until yesterday. Haven't done any major change or update, at least on my Linux partition (dual boot). But, I don't think that this has anything to do with that.  Any idea how can I fix this issue?  . Finding a 2x2 Matrix raised to the power of 1000 Let $A= \pmatrix{1&amp;4\\ 3&amp;2}$. Find $A^{1000}$.  Does this problem have to do with eigenvalues or is there another formula that is specific to 2x2 matrices? How do I technobabble without sounding like technobabble? "Each of these is" vs. "each of these are" Each of these CDFIs are finding solutions for communities that lack   access to traditional financial products and services, and the NEXT   Awards will accelerate their success.   OR     Each of these CDFIs is finding solutions for communities that lack   access to traditional financial products and services, and the NEXT   Awards will accelerate their success.   The difference is, the first one uses "CDFIs are" and the 2nd sentence uses "CDFIs is"  Which one is correct? Any why? What is *Cell standby* and how can I keep it from eating my battery? Looking up my battery statistics, I almost always find Cell standby amongst the top consumers:    I never thought that "idle" would use so much energy. I saw that other people encounter similar problems:       Answers on those questions just give some raw ideas. I would like to know what exactly stands behind this, an whether there are ways to keep this "standby" from eating my battery? A word for "intimate friends" without any kind of romance? I'm looking for a word to describe that a particular situation where two people (a man and a woman) are probably the best of friends but have no romantic inclinations towards each other. They may invade each others thoughts periodically but aren't really in a relationship per se. What would be a good word to describe this?  I'm aware of "platonic" but am wondering if there is another word? 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;  } The most efficient way to implement an integer based power function pow(int, int) Route AJAX failure messages to console instead of popup How can I prevent ajax failure popups and instead route the failure to the console log instead?  Is this something I can do with Drupals implementation of jQuery?