How can i calculate this combinations sum?
How to prove this binomial identity $\sum_{r=0}^n {r {n \choose r}} = n2^{n-1}$?
sed : Ignore line starting whitespace for match I want to replace the default listening port of httpd to 9090. I can edit the line in httpd.conf file using below  sed -i "/^Listen/c\Listen 9090" /etc/httpd/conf/httpd.conf   But the line   Listen 80   may have white space before it.  How do I ignore this white space to match this line? Visit to US before F1 using the Visa Waiver Program I am going to start a phd at the US with an F1 visa. University told me that I could enter the US only 30 days before the date on I-20. Since English is not my first language (and this would be a big change in my life) I would like to go there by June.  The thing is that I have an European passport with a valid ESTA. My plan would be to arrive with this passport, stay 4-6 weeks , go to Canada for a short vacation (maybe flight maybe by land) and come back to the USA with F1 visa.  I have two questions about this:  1) is this possible?   2) If yes, how could I justify knowing I will lose my come-back flight during my first entry? (I would purchase round trip because one-way are too expensive, probably with less than 90 days difference) Showing that $ \sum_{n=1}^{\infty} \arctan \left( \frac{2}{n^2} \right) =\frac{3\pi}{4}$ Why couldn't Bond have backup at the battle of Skyfall? I think I am missing a key plot point here.   Bond had to fake-kidnap M and bring her to Skyfall in order to lure Silva there for one last stand. Why did this have to be a secret from his colleagues at MI6? Why couldn't there have been other agents there to help defend the house and take down Silva?  Also, why did he have to have Q lay a fake trail to get Silva to follow him to Skyfall when he was actually going there, and he wanted Silva to follow him? Stone-Weierstrass theorem with $p(1/x)$ I am trying to prove that for a continuous $f\colon[1,\infty)\rightarrow\mathbb R$ and $f(x)\to a$ as $x\to\infty$ it could be approximated by $g(x)=p(1/x)$ where $p$ is a polynomial. I watched a video on youtube (I lost it) that shows rendering parts of the screen to combine them in a single image. I followed it to the point where I couldn't adjust the dimensions under the "set render border", but in the video he had dimensions and I have nothing.  I need it for 4K and 8K renders (without anti-aliasing), but my laptop can't handle it all at once and I don't have time for a 4 hour waiting so this feature will work perfectly.  I'm using version 2.76 so is it moved to another place or removed. Maybe a bug? I have the following ammeter:   The seller recommends 75mV 100A shunt be placed with it. I want to know what will happen if I change the voltage going through the shunt. Should I be changing the shunt as well to read amps correctly?   I want to build a 1-40V (or maybe 50V) adjustable DC power supply and use this ammeter to measure current. What the right value of shunt that I should use to get the right measurement? Changing shunts in a lab bench power supply is impractical, of course.  EDIT: I am planning to measure only up to 5A or so. Sorry I forgot to mention this previously. How to distribute proprietary Mathematica code Geometric series for two-point function In deriving the expression for the exact propagator  $$G_c^{(2)}(x_1,x_2)=[p^2-m^2+\Pi(p)]^{-1}$$   for $\phi^4$ theory all books that i know use the following argument:  $$G_c^{(2)}(x_1,x_2)=G_0^{(2)}+G_0^{(2)}\Pi G_0^{(2)}+G_0^{(2)}\Pi G_0^{(2)}\Pi G_0^{(2)}+...$$  wich is a geometric series so the formula for the exact propagator.Here  $$G_0^{(2)}$$   is the free propagator and   $$\Pi=X+Y+Z+...+W$$  is the sum of all irreducible diagrams.Here the irreducible diagrams is represented by $X,Y,Z,...,W$.  Using the path integral i can see, that  connected diagrams $D$ can be written in the form  $$D=G_0^{(2)}XG_0^{(2)}Z...G_0^{(2)}W$$  Question: But how to prove that there is no constant $C$ so that instead we have  $$D=G_0^{(2)}XG_0^{(2)}Z...G_0^{(2)}W$$  we would have  $$D=CG_0^{(2)}XG_0^{(2)}Z...G_0^{(2)}W~?$$  In the last case we would not have a geometrical serie. Can someone explain me i t please  or give me another way to derive it. I want to create a DEB file manually. I would like to just provide a folder which contains data to install, and a script to be executed after installation.  Is this possible? How to deploy wsp to single web application Graphics file extensions and their order of inclusion when not specified When using 's \includegraphics you can specify the file extension or not. For generic use and perhaps portability, extensions are commonly dropped. The types of "approved" inclusions and their order of precedence depends on the driver/compiler being used. What are these driver-defaults?  Related: Possible to save a list template and maintain lookup relationships? My issue is that I have two lists that I would like to move with their data.  While I am able to save both as templates and then upload to the new site, none of the lookup columns in my parent table are populated with data now.  Can this be done? 16.04 new installation gives grub-efi-amd64-signed failed installation /target/ ubuntu 16.04 at the end build argument lists containing whitespace In bash one can escape arguments that contain whitespace.  foo "a string"   This also works for arguments to a command or function:  bar() {     foo "$@" }  bar "a string"   So far so good, but what if I want to manipulate the arguments before calling foo?  This does not work:  bar() {     for arg in "$@"     do         args="$args \"prefix $arg\""     done      # Everything looks good ...     echo $args      # ... but it isn't.     foo $args      # foo "$args" would just be silly }  bar a b c   So how do you build argument lists when the arguments contain whitespace? How to disable the skype ads (advertisement)? Why did Dumbledore drink the potion in the attempt to get a Horcrux? When Albus Dumbledore  finally reaches the island with Harry Potter and finds out that you can't get near the potion, he made a cup and drank it. Why couldn't he just have poured the potion on the "floor"? Why couldn't he have made a big cup to hold almost everything inside the basin? If a drive doesn't know about partitions and files systems why moving a file from one partition to another takes relatively long time, unlike the instantaneous move on the same partition? Is that file system inefficiency? In this case, NTFS. It seems like the file is being copied and then original is erased, instead of removing the entry about that file in one partition and making it in another? I want a to be rounded to 13.95.  &gt;&gt;&gt; a 13.949999999999999 &gt;&gt;&gt; round(a, 2) 13.949999999999999   The  function does not work the way I expected. Remember all opened files with split windows and their positions in Emacs