Show the closed form of the sum $\sum_{i=0}^{n-1} i x^i$
How to compute the  formula $\sum  \limits_{r=1}^d r \cdot 2^r$?
Can I clear an area of my prison for everyone BUT max security prisoners? What is the name of the vertical bar in $(x^2+1)\vert_{x = 4}$ or $\left.\left(\frac{x^3}{3}+x+c\right) \right\vert_0^4$? I've always wanted to know what the name of the vertical bar in these examples was:  $f(x)=(x^2+1)\vert_{x = 4}$ (I know this means evaluate $x$ at $4$) $\int_0^4 (x^2+1) \,dx = \left.\left(\frac{x^3}{3}+x+c\right) \right\vert_0^4$ (and I know this means that you would then evaluate at $x=0$ and $x=4$, then subtract $F(4)-F(0)$ if finding the net signed area)  I know it seems trivial, but it's something I can't really seem to find when I go googling and the question came up in my calc class last night and no one seemed to know. Also, for bonus internets; What is the name of the horizontal bar in $\frac{x^3}{3}$? Is that called an obelus? Prerequisites for Algebraic Geometry Is it possible to get into algebraic geometry by just knowing calculus and linear algebra or is this too far of a stretch?  If not could anyone give me a list of book/lecture notes recommendations in chronological order to dive into algebraic geometry with my state of knowledge?  Thanks After upgrading to 12.04 from 10.04, can't login to PHPMYADMIN To my amazement I just discovered that the C99 stdint.h is missing from MS Visual Studio 2003 upwards.  I'm sure they have their reasons, but does anyone know where I can download a copy?  Without this header I have no definitions for useful types such as uint32_t, etc. Mask and convert color in photo/video I am very new to blender still.  I want to simply change the color of an object in the video.  I want to know if there is good way to do this.  I am including what I have to test. Expected Value Of Number of Removals From Urn Here's the question: "An urn contains b blue balls and r red balls. You repeatedly and independently remove balls from urn (without returning them) until the first blue ball is drawn. All balls currently in the urn have an equal probability of being selected each time a ball is removed. Define the random variable X as the number of balls that are drawn (number of red balls that are removed plus the first blue ball that is removed). Find E[X], the expected value of random variable X."  I'm having trouble finding a closed form expression for the expected value. Here's the work I've done: How can I calculate magnification ratio I get by reversing a lens? I am looking for a way to mathematically determine the maximum magnification ratio that is possible/practical to achieve by reverse mounting a non-macro lens, prior to purchasing the lens.     See related questions: Weird syslog order Have you ever seen wrong order in /var/log/syslog ? I think that it causes only crontab.  Jun 28 22:20:01 alex CRON[2327]: (root) CMD (something &gt; /dev/null) Jun 28 22:21:01 alex CRON[2700]: (root) CMD (something &gt; /dev/null) Jun 21 03:49:01 alex CRON[2753]: (root) CMD (something &gt; /dev/null) Jun 28 22:23:01 alex CRON[2754]: (root) CMD (something &gt; /dev/null) Jun 27 05:08:01 alex CRON[2813]: (root) CMD (something &gt; /dev/null) Jun 26 00:19:01 alex CRON[2816]: (root) CMD (something &gt; /dev/null) Jun 28 22:25:01 alex CRON[2816]: (munin) CMD (if [ -x /usr/bin/munin-cron ]; then /usr/bin/munin-cron; fi) Jun 28 22:25:01 alex CRON[2821]: (root) CMD (something &gt; /dev/null) Jun 28 22:27:01 alex CRON[3225]: (root) CMD (something &gt; /dev/null) Jun 28 22:28:01 alex CRON[3240]: (root) CMD (something &gt; /dev/null) Jun 28 22:30:01 alex CRON[3290]: (root) CMD (something &gt; /dev/null) Jun 26 12:03:01 alex CRON[3291]: message repeated 2 times: [ (root) CMD (something &gt; /dev/null)] Jun 28 22:30:01 alex CRON[3291]: (munin) CMD (if [ -x /usr/bin/munin-cron ]; then /usr/bin/munin-cron; fi) Jun 28 22:31:01 alex CRON[3659]: (root) CMD (something &gt; /dev/null) Jun 28 22:32:01 alex CRON[3754]: (root) CMD (something &gt; /dev/null) Jun 16 06:41:01 alex CRON[3846]: (root) CMD (something &gt; /dev/null) Jun 28 22:35:58 alex cron[909]: (CRON) INFO (pidfile fd = 3) Jun 28 22:35:58 alex cron[944]: (CRON) STARTUP (fork ok) Jun 28 22:35:58 alex cron[944]: (CRON) INFO (Running @reboot jobs) Jun 28 22:36:01 alex CRON[1428]: (root) CMD (something &gt; /dev/null) Jun 28 22:37:01 alex CRON[3050]: (root) CMD (something &gt; /dev/null) Jun 28 22:38:01 alex CRON[3082]: (root) CMD (something &gt; /dev/null) Jun 28 22:39:01 alex CRON[3114]: (root) CMD (something &gt; /dev/null)   As you can see, there is bad time order between lines. It is just crontab error, or there is some problem with system clock, or something?  I am running the latest Ubuntu 14.04 kernel:  Linux alex 3.13.0-30-generic #54-Ubuntu SMP Mon Jun 9 22:45:01 UTC 2014 x86_64 x86_64 x86_64 GNU/Linux How do i make my ubuntu server public? I want to know how to make my ubuntu server ip public. I'm not asking for a domain, if people would be able to access my website by ip, it would be great! (just for now) Does someone have an idea how to do this? I am an Indian citizen, holding a residence permit in Norway valid for 2 years. I want to know about the 90/180 rule.   Can I travel to Portugal for one week, come back to Norway and travel again for vacation for 2 weeks to Italy, and again come back to my residence country?  Does time spent in my residence country also count against my total stay in the Schengen area? Does Iit mean that the clock stops tickkng when person comes back to their residence country? The following code helps me validate an XML file with an XSD schema.  XmlReaderSettings settings = new XmlReaderSettings(); settings.Schemas.Add(null, xsdFilePath); settings.ValidationType = ValidationType.Schema; settings.ValidationEventHandler += new System.Xml.Schema.ValidationEventHandler(settings_ValidationEventHandler); XmlDocument document = new XmlDocument(); document.Load(xmlFilePath); XmlReader rdr = XmlReader.Create(new StringReader(document.InnerXml), settings);  while (rdr.Read()) {  } isValid = true;   The ValidationEventHandler also tells me what the errors are, but doesn't tell me on 'where' or 'on which line' they are located. Is there any way to get the line number where the XML fails to be validated? Proof Check: Every Cauchy Sequence is Bounded Sorry if I keep asking for proof checks. I'll try to keep it to a minimum after this. I know this has a well-known proof. I understand that proof as well but I thought I'd do a proof that made sense to me and seemed, in some ways, simpler. Trouble is I'm not sure if it's totally correct. It's quite short though. I was just hoping someone could look it over and see if it is a valid proof. Thank you!  Lemma: Every Cauchy sequence is bounded.  Proof: Let $(a_{n})$ be Cauchy. We choose $ 0&lt;\epsilon_{0}$. So $ \forall \; n&gt;m\geq N_{0}$ we have that $\vert a_{n}-a_{m} \vert &lt; \epsilon_{0}$. Therefore $(a_{n})$ is bounded for all $ m \geq N_{0} $ by $ \epsilon_{0} $. Since $ \mathbb{N}_{N_{0}}$ is finite, it is bounded. So, for all $ m&lt;N_{0} $, $ (a_{n})$ is bounded. Therefore $(a_{n})$ is bounded.  I realize I haven't said what the bounds are but I think that's sort of irrelevant. So long as we know it's bounded. Any help is much appreciated! Are PHP short tags acceptable to use? Two of my friends are getting married. They're both huge Doctor Who geeks, and actually met through a DW RPG. Their wedding invitation contained a very subtle DW reference (you wouldn't have been able to tell unless you were very familiar with the show yourself.)   Doctor Who's been running long enough that there are quite a few nice quotes for basically every occasion in life. I was hoping someone would know a nice wedding-related one, or maybe one about love, that I could include in a wedding card? I'm entering the world of Linux and at work I'm using grep more and more.  By doing that I'm figuring out that sometimes it's not adequate for what I want.  I was struggling with grep a few days ago and a colleague of mine who is a senior Linux admin, told me to use awk. I was stunned by how fast I got a result.  So my question is when do you choose to use one over the other? What questions can I ask myself before going to work with grep and spending a lot of time, when I could have done it with awk and saved time? Since , how do I uninstall it from my desktop system?  (Please note: This question is not about Unity 7, which is still supported at the time of this writing and should remain installed if present.) Prove that if every node in a simple graph $G$ has degree $3$ or higher, then $G$ contains a cycle with a chord. OR-ing power supplies (diode or mosfet) I have got two power supply options on my board:   USB 5.0V DC Power Jack of 5.0V   My intention is to design a or-ing power supply option, as either of them will be used at a time. Possible solutions are shown below:    Using oring diodes   or using two p-mos    Possible issues observed with the above options:   Using diode is cheap and good option but an ordinary diode gives a drop of 0.7V and a schottky diode will give a drop of 0.16 to 0.20 volts, which is also not acceptable because my processor  recommended operating power supply is 5.0V and minimum supply voltage is 4.75. With a 0.2V with schottky diode the 5.0V comes down to 4.80V and the space between recommended and supply fed is very less. Then I thought to use p-mosfets which serves the purpose of oring along with reverse polarity protection, but assume a case when both the supplies are fed together by mistake and there is minor difference between USB supply and DC jack say 4.9V for USB and 5.10V for DC Jack. Then, the DC jack supply may pump the current in USB Jack, which may damage USB.   Is there any other better and cheap option I should use for or-ing supply, or is there something wrong with my analysis? I've always been taught to put myself last when referring to myself in the same sentence as others but the usage of "me and..." seems to be everywhere these days. The misuse of the word "me" instead of "I" aside, is there some new rule I haven't heard of? Shouldn't we put ourselves last regardless of the "me"/"I" usage?  Examples of "correct" usage:      My friends and I went for some ice   cream. Did you see my friends and me   at the ice cream stand?   Examples of "incorrect" usage:     Me and my friends went for some ice   cream. Did you see me and my friends   at the ice cream stand?   Note: I was also taught that the only person who could put themselves first was the queen.