Proving this inequality $\left(1+\frac{1}{n}\right)^n < 3$
Inequality $(1+\frac1k)^k \leq 3$
101 positive integers placed on a circle A Pigeonhole Principle problem:     101 positive integers are placed on a circle whose sum is 300. Prove   that it is possible to choose from these numbers some consecutive   numbers whose sum is equal to 200.   (I don't know if the word 'consecutive' is appropriate in this case ,I mean that these numbers follow each other on that circle) Supporting Multiple Screen Sizes in Storyboards (3.5 and 4 inch screens) Why don't Muggle-born wizards use Muggle technology to fight Death Eaters? Align multiline equation with expression after equal sign I am trying to align a multiline equation using array within the equation but it turns out it doesn't do very well. The code I am using is as follows:  \begin{equation}    \begin{array}{lcl} \mathcal{L}^{-1}\left\{f(d)\right\} &amp;= \mathcal{L}^{-1}\left\{f_1(\delta).f_2(\delta)\right\} \\ &amp; = exp(mt) \star \left\{\frac{l}{2\sqrt{\pi t^3}} exp(-l^2/{4t})\right\} \\ &amp; = F_1 * F_2 \end{array} \end{equation}   Can anyone suggest better way to deal with it ? Combining two expressions (Expression>) I have two expressions of type Expression&lt;Func&lt;T, bool&gt;&gt; and I want to take to OR, AND or NOT of these and get a new expression of the same type  Expression&lt;Func&lt;T, bool&gt;&gt; expr1; Expression&lt;Func&lt;T, bool&gt;&gt; expr2;  ...  //how to do this (the code below will obviously not work) Expression&lt;Func&lt;T, bool&gt;&gt; andExpression = expr AND expr2 True or false: {{∅}} ⊂ {∅,{∅}} Recover files from hard drive that has been formatted thrice I have a situation.  I got married 6 months ago and stored some very important pictures on my laptop which was running Linux. Later I formatted the whole hard drive, installed Windows and a hacked version of Mac (just to play around) and I have been using the laptop for last 8 months or so after that.  Is there any software that can recover the files for me? I am happy to pay money! How do I find the current machine's full hostname in C (hostname and domain information)? In a C project (POSIX), how do I get the fully qualified name for the current system?  For example, I can get just the hostname of my machine by doing gethostname() from unistd.h. This might give me machine3 in return, but I'm actually looking for machine3.somedomain.com for example.  How do I go about getting this information? I do not want to use a call to system() to do this, if possible. Suppose $\displaystyle P(x,y)$ a polynomial in the variables $x,y$.   For example, $\displaystyle x^4$ or $\displaystyle x^3y^2 + 3xy + 1$.  Is there a general method which allows us to evaluate the indefinite integral     $$ \int P(\sin x, \cos x) \text{d} x$$   What about the case when $\displaystyle P(x,y)$ is a rational function (i.e. a ratio of two polynomials)?   Example of a rational function: $\displaystyle \frac{x^2y + y^3}{x+y}$.    This is being asked in an effort to cut down on duplicates, see here:   and here: Add a dependency in Maven Most modern texts spend some time deriving the  that connects S matrix elements to time ordered field correlation functions. It seems essential, and really helps clear up what you are calculating. Yet some earlier texts and even some modern texts (e.g.  by R. Klauber) seem to skip right past this, working everything out in the "interaction" picture. It seems there must be something going wrong with this latter procedure, but I am not quite able to put it together. I am creating a chat using Ajax requests and I'm trying to get messages div to scroll to the bottom without much luck. I am wrapping everything in this div: #scroll {     height:400px;     overflow:scroll; }  Is there a way to keep it scrolled to the bottom by default using JS? Is there a way to keep it scrolled to the bottom after an ajax request? OS keyboard shortcuts conflict with apps keyboard shortcuts in GNOME 3 I have Ubuntu 16.04 with GNOME shell. I set ctrl+shift for the "Modifiers-only switch to next source" option.   This shortcut conflicts with apps hot-keys. I can't use ctrl+shift+i to open devtools in Chrome, it just switches the layout. In VS code IDE if I press shortcuts with ctrl+shift (for example ctrl+shift+f), shortcuts work but always switch a keyboard layout. When I used Windows this problem didn't exist.  Can I set the ctrl+shift shortcut in such a way that it causes a switch action only after the keys are released and only if this 2 keys were pressed (without additional keys)? I think the term "back and forth" gets thrown around a lot without much thought.  From Dictionary.com:         [fawrth, fohrth]      adverb    1.  onward or outward in place or space; forward: to come forth; go forth.   Wouldn't the term be more meaningful if "forth" was used first since you have to have a starting place before you can go "back"?  Examples:        I've been going back and forth from Houston to New York.   I've been going forth and back from Houston to New York.      Which is more correct? I am given that $V$ is n-dimensional vector space over $\mathbb{C}$ and $T \in L(V)$. And $T$ has least $m$ distinct nonzero eigenvalues. How do I show that $\text{null}(T^{n-m}) = \text{null}(T^{n-m+1})$?  I'm really not sure how to start here so just the first couple steps would be very helpful. Thanks!! Can I prevent/restrict standard users from installing/uninstalling software? Can i prevent/restrict standard user from installing/uninstalling software in Ubuntu 12.04 desktop? Using Windows 10 in a virtual machine. Can it be done? I am currently running 8.1. I'd like to try out Windows 10 and if I like it upgrade. If not, I'll keep running as I am.   I've never used a virtual machine before: can Window 10 be used from a virtual machine as a "sandbox", and if so how? What do I if I used "Reset All" or "Erase All Content and Settings" on a jailbroken iOS Device? I recently received an iOS device and it was jailbroken. When I wanted to unjailbreak it, I used "Erase All Content and Settings." The loading screen came on and it has not changed. After rebooting the device, it is now stuck at the Apple logo. What should I do? Remove GRUB and keep a Linux system Network button missing gone from Nautilus? I'm using Ubuntu 16.04.3 LTS.  I remember having a link in Nautilus that I used to browse network shares with in the past. I don't remember exactly but I think it was "Windows network" or "Browse network".  Now I can't find this on my current installation, there's only "Connect to server", but this is not what I want. Is there a way to put that link there?