"me and the other" or "I and the other"?
Which is more formal: "My parents will reside with me and my family" or "my family and I"?
How to find answer to the sum of series $\sum_{n=1}^{\infty}\frac{n}{2^n} $ I have put his on wolfram and obtained answer as follows:  $\sum_{n=1}^{\infty}\frac{n}{2^n} = 2$  And the series is convergent too because $\lim_{n\to\infty} \frac {n}{2^n} = 0$  However I am wondering if there is a convenient way to solve this; I don't think you can represent it by a geometric progression either. So how do we have to do it on paper? With lots of guides and setup variations all over the internet, I find it confusing which is which to really follow. Normally, in Windows 8 my setup would be install everything in the HDD and use Intel Smart Response for a speedy setup. However as I am new to Linux I really don't know what to do.  My ideal setup would be something similar to this, but I know for a fact that IRST is not available in Linux so what I intend to do is keep the OS files in the SSD instead and keep my media on the larger HDD. A step by step procedure would be extremely helpful.     Edit: I want a system running solely on Ubuntu, with the SSD to speed things up but setting it in such a way that it does not hasten its lifespan.    # /etc/fstab: static file system information.  # # Use 'blkid' to print the universally unique identifier for a  # device; this may be used with UUID= as a more robust way to name devices  # that works even if disks are added and removed. See fstab(5).  #  # &lt;file system&gt; &lt;mount point&gt; &lt;type&gt; &lt;options&gt; &lt;dump&gt; &lt;pass&gt;  # / was on /dev/sda1 during installation  UUID=80289460-5983-4349-8afc-6f3119938ee9 / ext4 errors=remount-ro 0 1   # /files was on /dev/sdb5 during installation  UUID=c1678c88-5100-41bc-8090-7887f1622c7f /files ext4 defaults 0 2   # swap was on /dev/sdb6 during installation  UUID=608e3ec2-c76e-4657-af6d-80793b5f50f6 none swap sw 0 0 I am considering trying to setup a  system. It seems like this would be pretty straight forward if I had two graphics cards or if I didn't need hardware based OpenGL acceleration. Is it possible to setup a multi seat system with only a single dual-headed graphics card? If $\int_0^x f \ dm$ is zero everywhere then $f$ is zero almost everywhere I have been thinking on and off about a problem for some time now. It is inspired by an exam problem which I solved but I wanted to find an alternative solution. The object was to prove that some sequence of functions converges weakly to zero in $L^2$.   I managed to show (with some help) that the limit $f$ (of a subsequence) satisfies $\int_0^x f \ dm=0$ for all $x&gt;0 $. From this I want to conclude that $f=0$ a.e. I can do this with the fundamental theorem of calculus in its Lebesgue version but there ought to be a more elementary proof.  Can someone here help me out? Adding a class to “body” I'm trying to add a custom CSS class to the &lt;body&gt; tag, How can I modify or pre-process the &lt;body&gt; tag to add the class body, Is it right to style the &lt;body&gt; tag with css file? Let $G$ be abelian, $H$ and $K$ subgroups of orders $n$, $m$. Then G has subgroup of order $\operatorname{lcm}(n,m)$. How do I detect the direction of 2D rectangular object collisions? traveller's cheques; customer's requirements: use of the singular Saxon genitive (and the plural attributive) for association May I ask if the following sentence is grammatical?      Our remit is to conduct research on customer's requirements.   In my understanding, as 'customer' is a countable noun, so the plural form 'customers''' should be used instead for this general reference (without specification of certain customers).   However, I know that we can say 'traveller's cheques' - e.g.,      Traveller's cheques are available at the bank.    In this sense, actually can we say 'customer's requirements' in the first case? I have a text file abc.txt and its contents are:     /lag/cnn/org/one.txt    /lag/cnn/org/two.txt    /lag/cnn/org/three.txt   If I use:  $ tar -cvf allfiles.tar -T abc.txt   I'm getting the tar of files in the list. Similarly is it possible to copy those files in abc.txt to a folder?  I tried this:              $ cp --files-from test1.txt ./Folder   But it is not working. If Newton's third law is true, why can we sink in sand? Newton's third law of motion states that every action has an equal and opposite reaction. That is the reason we do not sink into the earth, because when our weight exerts a force on the earth it also exerts an equal and opposite force on us.  But when we stand on quicksand or on fluids we can sink in. How is this possible? Does it not exert an equal and opposite force on us? Or are Newton's laws different in the case of fluids and substances of low densities? Let $f:X \to Y$ be a homeomorphism between topological spaces $X$ and $Y$. Let $A \subseteq X$ and $B = f(A) \subseteq Y$ (given the subspace topology) and let $g: A \to B$ be the restriction of $f$ given by $g(a) = f(a)$ for $a \in A$.  Showing that $g$ is a homeomorphism.   $g$ injective   Let $g(a_1) = g(a_2)$, $a_1, a_2 \in A$.  $\implies f(a_1) = f(a_2)$  $\implies a_1 = a_2$ as $f$ homeomorphic.   g surjective   Let $y \in B$  $\implies y = f(a)$ for some $a \in A$.  $\implies y = g(a)$ for some $a \in A$.   $g$ continuous   Let $U \subseteq B$ be an open set in $B$.  $f(a) = g(a)$ for all $a \in A =&gt; f^{-1}(b) = g^{-1}(b)$ for all $b \in B$.  So $g^{-1}(U) = f^{-1}(U)$ which is open in $A$ as $f$ homeomorphic.   $g^{-1}$ continuous   Let $U \subseteq A$ be an open set in $A$.  $g(U) = f(U)$ which is open in $B$ as $f$ homeomorphic.  So $g$ is homeomorphic.  Is my understanding correct, this seems almost too straightforward so I was wondering have I overlooked something? Given three matrices $A$, $B$ and $C$ such that $ABA^T C$ is a square matrix, the derivative of the trace with respect to $A$ is:  $$ \nabla_A \operatorname{trace}( ABA^{T}C )  = CAB + C^T AB^T $$  There is a proof . However, I was not able to understand the second line of the proof. it says something like this:  $$ \nabla_A \operatorname{trace}( ABA^T C )= \nabla_\bullet \operatorname{trace}(f(\bullet)A^{T}C) + \nabla_\bullet \operatorname{trace}(f(A) \bullet^T C) $$  Where  $f(A) = AB$  I tried searching the proof or any hint using google, but I couldn't fine anything. Could anyone please help me with this second line. I cannot sleep. I am obsessed with this proof. Why was mixing declarations and code forbidden up until C99? Verbless sentence I thought I heard my teacher said: 'Don't construct a sentence without a verb.'  Is there such rule in english grammar?     She looks like 70 years old. Perhaps older.   How about the question above? Is it correct? Is there any book that can be used references for wide range of topics in grammar(including syntax, morphology et cetera)? I have finished oxford grammar in use recently and think it wasn't enough for me. How do AD/AP boosts apply to abilities with long cast times, channels or animations? For example: I'm playing Janna in bot lane with Caitlyn. Caitlyn begins channeling Ace in the Hole to finish off an enemy. Will the AD buff from my Eye of the Storm apply extra damage to Caitlyn's ultimate if I cast at after she begins channeling? Similarly, if I see Caitlyn rev up to shoot Piltover Peacemaker, can I boost her AD after the animation begins? (If I remember correctly, Piltover Peacemaker has a quick cast time, but the spell animation is rather long, so it may be a different circumstance from the first example.)  Basically, I want to know if the AD is calculated at the start of a cast, at the end of a cast, or when the ability actually creates and object on the battlefield. I have a list of items   John ID Matt ID John ID Scott ID Matt ID John ID Lucas ID   I want to shove them back into a list like so which also means I want to sort by the highest number of duplicates.   John ID 3 Matt ID 2 Scott ID 1 Lucas ID 1   Let me know how I can do this with LINQ and C#.  Thanks All  EDIT 2 Showing Code:      List&lt;game&gt; inventory = new List&lt;game&gt;();     drinkingforDataContext db = new drinkingforDataContext();     foreach (string item in tbTitle.Text.Split(' '))     {          List&lt;game&gt; getItems = (from dfg in db.drinkingfor_Games                                where dfg.game_Name.Contains(tbTitle.Text)                                select new game                                {                                    gameName = dfg.game_Name,                                    gameID = Boomers.Utilities.Guids.Encoder.EncodeURLs(dfg.uid)                                }).ToList&lt;game&gt;();          for (int i = 0; i &lt; getItems.Count(); i++)         {             inventory.Add(getItems[i]);         }     }      var items = (from xx in inventory                  group xx by xx into g                  let count = g.Count()                  orderby count descending                  select new                     {                         Count = count,                         gameName = g.Key.gameName,                         gameID = g.Key.gameID                     });      lvRelatedGames.DataSource = items;     lvRelatedGames.DataBind();   This query displays these results:   1 hello world times 1 hello world times 1 Hello World. 1 hello world times 1 hello world times 1 hello world times 1 Hello World. 1 hello world times   It gives me the count and name, but it doesn't give me the ID of the game....  It should display:   6 hello world times   234234 2 Hello World.  23432432 Let $f \colon \mathbb{R} \rightarrow  \mathbb{R}$ be a smooth function such that $$f'(x) = f(1+x)$$ How can we find the general form of $f$? I thought of some differential equations, but not sure how to use them here. Thanks. I want to set an environment variable from the command prompt and then be able to access it globally (for instance, I should see it by going to System -> Environment Variables).    When I use the set command, it isn't accessible in a new cmd session.  set NEWVAR=SOMETHING echo %NEWVAR%   Related questions: How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$? "Unfortunately, ... has stopped" when Downloading file in Android