Sum of series (1 + (y/m) + (y/m)^2 + ... + (y/m)^n)
Partial Sums of Geometric Series
Is any aspect of the supernatural testable? What level of proof is possible for the supernatural? How to divide LaTeX table cells vertically? I want my table to have separated cells. Basically double lines but I can't figure how to have horizontal lines disconnected. I tried \hline and \cline but those connect too.  This is best I can do:    This is how I want my table to look:   \begin{tabular}{|c||c||c||c|}   \hline   \multicolumn{2}{|c||}{First Cell}&amp;   Second Cell&amp;   Third Cell\\   \hline   \hline   \begin{tabular}{@{}l@{}} Data\\ Data\\ Data\\   \end{tabular}&amp;   \begin{tabular}{@{}l@{}}     Data\\     Data\\     Data\\   \end{tabular}&amp;   \begin{tabular}{@{}l@{}}     Data\\     Data\\     Data\\   \end{tabular}&amp;   \begin{tabular}{@{}l@{}}     Data\\     Data\\     Data\\   \end{tabular}\\    \hline  \end{tabular} Resize multiple layers around their respective anchor points Why does factoring eliminate a hole in the limit? How to set up USB for Virtualbox? I'm using Ubuntu Maverick and Virtual Box 3+. I have Windows 7 Ultimate. The problem is that it doesn't detect USB drives in Windows 7, but USB peripherals (mouse + keybord) are working.  I followed , but I can't find the user group vboxusers. How can I continue? I would also like to upgrade to the latest version without any risk (without losing my virtual hard disk drive). I needed to change the SID of an Oracle XE database (not the Service Name) to match a production database.  When I tried searching online, most of the pages were describing changing or adding a service name through tnsnames.ora; that's not what I needed to do. What is *.pkinfo file? What is a *.pkinfo file?   Google Search results talk about Package Info files and how they contain map documents and layers, so I don't see how this is different from a .mpk file.    I also have not found anything about how to create a *.pkinfo file. I would like to manipulate the HTML inside an iframe using jQuery.  I thought I'd be able to do this by setting the context of the jQuery function to be the document of the iframe, something like:  $(function(){ //document ready     $('some selector', frames['nameOfMyIframe'].document).doStuff() });   However this doesn't seem to work. A bit of inspection shows me that the variables in frames['nameOfMyIframe'] are undefined unless I wait a while for the iframe to load. However, when the iframe loads the variables are not accessible (I get permission denied-type errors).  Does anyone know of a work-around to this? I have a laptop with win7 installed. I have now made a 60gb partition which I want to install ubuntu into. The question I have, before I do the installation, is how large each of the root, swap, and home partition should be? I have read some place that root could be as small as 8GB, but isn't that too small? Since I guess beside ubuntu all the softwares installed will reside there as well? And I think I'm going to set my swap to be 2GB large.  My main concern is how large should the root partition should be. I'm mainly going to use ubuntu for programming and browse the web. I'm getting "jumpy" loadings in rollapply PCA in R. Can I fix it? I have 10 years of daily returns data for 28 different currencies. I wish to extract the first principal component, but rather than operate PCA on the whole 10 years, I want to rollapply a 2 year window, because the currencies' behaviours evolve and so I wish to reflect this. However I have a major problem, that is that both the princomp() and prcomp() functions will often jump from positive to negative loadings in adjacent PCA analyses (ie 1 day apart). Have a look at the loading chart for the EUR currency:    Clearly I can't use this because adjacent loadings will jump from positive to negative, so my series which uses them will be erroneous. Now take a look at the absolute value of the EUR currency loading:    The problem is of course that I still cannot use this because you can see from the top chart that the loading does go from negative to positive and back at times, a characteristic which I need to preserve.   Is there any way I can get around this problem? Can I force the eigenvector orientation to always be the same in adjacent PCAs?   By the way this problem also occurs with the FactoMineR PCA() function. The code for the rollapply is here:  rollapply(retmat, windowl, function(x) summary(princomp(x))$loadings[, 1], by.column = FALSE, align = "right") -&gt; princomproll 'sudo su -' vs 'sudo -i' vs 'sudo /bin/bash' - when does it matter which is used, or does it matter at all? When I'm doing something that requires root be typed in dozens of times in a row, I prefer to switch my session to a root session. In the various tutorials and instructions I have used on the Internet, I see sudo su, sudo su -, sudo -i and sudo /bin/bash being used to open a root session, but I'm not clear on the difference between these and when or if that difference matters.  Can someone clear this up for me? This is a  about CNAMEs at the apices (or roots) of zones   It's relatively common knowledge that CNAME records at the apex of a domain are a taboo practice.  Example: example.com. IN CNAME ithurts.example.net.  In a best case scenario nameserver software might refuse to load the configuration, and in the worst case it might accept this configuration and invalidate the configuration for example.com.  Recently I had a webhosting company pass instructions to a business unit that we needed to CNAME the apex of our domain to a new record. Knowing that this would be a suicide config when fed to BIND, I advised them that we would not be able to comply and that this was bunk advice in general. The webhosting company took the stance that it is not outright forbidden by standard defining RFCs and that their software supports it. If we could not CNAME the apex, their advice was to have no apex record at all and they would not provide a redirecting webserver. ...What?  Most of us know that  insists that A CNAME record is not allowed to coexist with any other data., but let's be honest with ourselves here, that RFC is only Informational. The closest I know to verbiage that forbids the practice is from :     If a CNAME RR is present at a node, no other data should be   present; this ensures that the data for a canonical name and its aliases   cannot be different.   Unfortunately I've been in the industry long enough to know that "should not" is not the same as "must not", and that's enough rope for most software designers to hang themselves with. Knowing that anything short of a concise link to a slam dunk would be a waste of my time, I ended up letting the company get away with a scolding for recommending configurations that could break commonly used software without proper disclosure.  This brings us to the Q&amp;A. For once I'd like us to get really technical about the insanity of apex CNAMEs, and not skirt around the issue like we usually do when someone posts on the subject.  is off limits, as are any other Informational RFC applicable here that I didn't think of. Let's shut this baby down. nVidia driver reset after each kernel update I am using the official nVidia driver because my card (GeForce 750 Ti) isn't yet supported by the Ubuntu one. Every time the kernel updates, my system breaks.  I've formatted my system two-three times because of kernel updates and today I decided to try to fix it. I tried to fix it with this method and surprisingly it works.   Switch to console (After waiting for the nVidia driver to crash, as it does when you switch consoles :p) Run a complete uninstall  sudo ./&lt;DRIVER&gt;.run -uninstall  Reboot and switch to the on-board card Update  sudo apt-get update sudo apt-get dist-upgrade  Reboot again Reinstall driver  sudo ./&lt;DRIVER&gt;.run  Reboot and switch back to the NVIDIA GPU   Is there a better/easier/faster way to update without going through all this? Say i have this PHP code:  $FooBar = "a string";   i then need a function like this:  print_var_name($FooBar);   which prints:  FooBar   Any Ideas how to achieve this? Is this even possible in PHP? Let $(B_t)_{t\geq 0}$ be a standard Brownian motion in $\mathbb{R}^d$. It is intuitive that, for fixed $s&lt;t&lt;u$  $$\mathbb{E}[B_t\mid \sigma(B_s,B_u)]=B_s+\frac{t-s}{u-s}(B_u-B_s).$$  However, I cannot think of a way to show this rigorously.   If first attempted to take $A\in\sigma(B_s,B_u)$ and show that $\mathbb{E}[1_A B_t]=\mathbb{E}[1_A(B_s+\frac{t-s}{u-s}(B_u-B_s))]$. But I cannot manage to show this equality.   I'd be very thankful for any ideas and suggestions on how to tackle this problem. Error mounting NTFS partition after hybrid shutdown with Windows 8 I've got this error and I can't access my files located in a different partition when I'm using Ubuntu, but when I'm using Windows 8 my files are accessible. I'm using Ubuntu as my main OS. I tried shutting down Windows 8 properly but still nothing happened. Is there any way where this can be fixed?  Error mounting /dev/sda4 at /media/kris/BackUp Files:  Command-line `mount -t "ntfs" -o "uhelper=udisks2,nodev,nosuid,uid=1000,gid=1000,dmask=0077,fmask=0177" "/dev/sda4" "/media/kris/BackUp Files"' exited with non-zero exit status 14:  The disk contains an unclean file system (0, 0). Metadata kept in Windows cache, refused to mount. Failed to mount '/dev/sda4': Operation not permitted The NTFS partition is in an unsafe state. Please resume and shutdown Windows fully (no hibernation or fast restarting), or mount the volume read-only with the 'ro' mount option. the method getApplicationContext() is undefined Can I revert to the Mountain Lion style labels instead of Mavericks tags? How? My understanding is that light can not escape from within a black hole (within the event horizon).  I've also heard that information cannot propagate faster than the speed of light.  It would seem to me that the gravitational attraction caused by a black hole carries information about the amount of mass within the black hole.  So, how does this information escape?  Looking at it from a particle point of view: do the gravitons (should they exist) travel faster than the photons? Debugging JavaScript in IE7 I need to debug JavaScript in Internet Explorer 7. Unfortunately, its default debugger doesn't provide me with much information. It tells me the page that the error showed up on (not the specific script) and gives me a line number.  I don't know if that is related to my problem. It'd be nice if it could narrow down the error to a line number on a specific script (like Firebug can). Is there an addon to debug JavaScript in IE7 like Firebug does in Firefox? Thank you! See also: