I know that my title was not very clear, but I do not know of any other way to describe this. I want to be able to write the following, and be able to change what letters are below the arrow:  Note: I have never used LaTeX, but the text editor that I am using supports it, and it seems to be my best bet. However if there is a better way to do it, I am not committed to LaTeX in any way.
I need a way of encoding the geometry line symbol. $\overline{AB}$ gives me the line segment symbol and $\overrightarrow{AB}$ gives me the ray symbol, I need a way to get a bar over the letters that has arrows on both ends. $\overrightleftarrow{AB}$ does not work.   Thanks!
Does the sequence $$\displaystyle \frac{n}{\sum\limits_{k=1}^{n}\Big(\frac{k}{k+1}\Big)^k}$$   converge?   Attempt. Since $\Big(\frac{k}{k+1}\Big)^k \rightarrow 1/e\neq 0$ and the terms are positive, the series $\sum\limits_{k=1}^{\infty}\Big(\frac{k}{k+1}\Big)^k$ diverges to $+\infty$. I find hard to determine if $n$ or the sum goes faster to $+\infty.$   Thanks in advance. Let's say I have a (comparatively) lovely-looking document in LaTeX, full of lovingly typeset, (relatively) complex equations. Now, let's say some barbarians come along one day and decide that the document has to be put into Microsoft Word (2007). ...after the usual mourning period associated with such events, let's say I value my job (more specifically, the bread it provides) enough to get all the text and tables formatted and references organised into the Word document. –...related questions  and – Now I'm looking at the equations with fear and dread. One option of course is to just lift screenshots from the original document, but this is painstaking if I need to refer to parts of the equation in the text. Also, I might need to edit equations on the fly. Anyone know of a free application which allows embedding LaTeX math into MS Word? I've looked at  and  which do roughly what I want... they build LaTeX images from source and embed them into the Word document, allowing to edit the source later... but both are commerical. ...any help in these troubling times will be greatly appreciated. EDIT: Just a note that  offers a 30-day free trial and is working out really nicely... but still, it's not free. Might be a good solution for those with short-term needs, or money. Showing group with $p^2$ elements is Abelian I have a group $G$ with $p^2$ elements, where $p$ is a prime number. Some (potentially) useful preliminary information I have is that there are exactly $p+1$ subgroups with $p$ elements, and with that I was able to show $G$ has a normal subgroup $N$ with $p$ elements.   My problem is showing that $G$ is abelian, and I would be glad if someone could show me how.   I had two potential approaches in mind and I would prefer if one of these were used (especially the second one).   First: The center $Z(G)$ is a normal subgroup of $G$ so by Langrange's theorem, if $Z(G)$ has anything other than the identity, it's size is either $p$ or $p^2$. If $p^2$ then $Z(G)=G$ and we are done. If $Z(G)=p$ then the quotient group of $G$ factored out by $Z(G)$ has $p$ elements, so it is cylic and I can prove from there that this implies $G$ is abelian. So can we show theres something other than the identity in the center of $G$?  Second: I list out the elements of some other subgroup $H$ with $p$ elements such that the intersection of $H$ and $N$ is only the identity (if any more, due to prime order the intersected elements would generate the entire subgroups). Let $N$ be generated by $a$ and $H$ be generated by $b$. We can show $NK= G$, i.e every element in G can be wrriten like $a^k b^l $. So for this method, we just need to show $ab=ba$ (remember, these are not general elements in the set, but the generators of $N$ and $H$).   Do any of these methods seem viable? I understand one can give very strong theorems using Sylow theorems and related facts, but I am looking for an elementary solution (no Sylow theorems, facts about p-groups, centrailzers) but definitions of centres and normalizers is fine. Difference between standard beta and unstandard beta distributions? What is the difference between standard beta and unstandard beta distributions? How to understand in an article if it is not described if it is standard or not? How do I install "non-free firmware" (wifi driver) from USB? (Debian) Just noticed the "meta user" link under the picture and reputation on the Stack Exchange user's page. It doesn't seem to work for all users. Error is "Page Not Found".   Not working:  /  Working:  /    My guess is this is because they've never logged into the meta site. I'm trying to run multiple Nodejs applications on Nginx server running on CentOS 7. I noticed that when I run a Nodejs app on some ports I get an 502 Bad Gateway error in the browser so I checked the error logs:  [notice] 12806#0: signal process started [crit] 12807#0: *13 connect() to 127.0.0.1:7777 failed (13: Permission denied) while connecting to upstream, client: **.**.99.58, server: myapp.com, request: "GET / HTTP/1.1", upstream: "http://127.0.0.1:7777/", host: "myapp.com" [crit] 12807#0: *13 connect() to [::1]:7777 failed (13: Permission denied) while connecting to upstream, client: **.**.99.58, server: myapp.com, request: "GET / HTTP/1.1", upstream: "http://[::1]:7777/", host: "myapp.com"   when I change the app to listen to 8008 for example everything is working fine. I checked permissions and if the process is running as root and everything seems ok. I played with the timeouts as well but no result. Can anyone help? Should we always override equals? Let f(t)=2/(t+8)  (a) Simplify the following difference quotient as much as possible: $$[f(t+h)−f(t)]/h$$  MY ANSWER (CORRECT): $-2 / [(t+8)(t+h+8)]$  (b) Use your result from (a) and the limit definition of the derivative to calculate $f′(t)=\lim_{h → 0} [f(t+h)−f(t)]/h=$  MY ANSWER (CORRECT): $-2 / [(t+8)^2]$  (c) Use your answer from part (b) to evaluate $f′(−3)$  MY ANSWER (CORRECT): $-2 / 25$  (d) Find the equation of the tangent line to the curve at the point $(−3,f(−3))$ y=  I have tried the point-slope formula, $y-y_1=m(x-x_1)$, but my answer was incorrect. It would seem that far-away stars are at such a distance that I should be able to take a step to the side and not have the star's photons hit my eye. How do stars release so many photons to fill in such great angular distances? .fbx export why there are no materials or textures? I used node textures in a mesh I exported to .FBX.  I then imported it into Unreal Engine 4 and it didn't import any textures; I clicked the Upload Textures option in Unreal Engine.  Is there something I'm doing wrong or is it Blender? Where is the preferred place to set the PATH envvar?  ~/.profile or /etc/environment?  What is the case when PATH is set in both places? Is the end result a concatenation of both values set in those two places? I would like to know how to find a set of coordinates on a small circle some distance from another point.   For example, lets say A = (39.73, -104.98) #Denver  B = (39.83, -106.06) #point approximately 50 nautical miles away from A along the great circle track to C  C = (40.75, -111.88) #Salt Lake City, approximately 323 nautical miles away from A  How do I get the set of orange coordinates when I don't know the angle but I do know the cross track distance?  For concreteness, lets say the outer points near B have a cross track distance of +- 30 nautical miles and the inner points have a cross track of +- 15nm.  And the points near C have a cross track of +- 25 nm.  Also I have an initial bearing from A to C of -1.34 #radians Elastic net penalty Given two date ranges, what is the simplest or most efficient way to determine whether the two date ranges overlap?  As an example, suppose we have ranges denoted by DateTime variables StartDate1 to EndDate1 and StartDate2 to EndDate2. Zsh get terminfo keys with modifiers Understanding the length extension attack I have been trying to understand exactly how a length extension attack works on SHA-1. I'll detail below what I've understood so far, so that I can convey my understanding of the same and hopefully get advice on where I'm going wrong.  Lets assume that for a message $m$, a secret $s$ is appended to it and the SHA-1 hash is calculated. If $\textrm{len}(m) + \textrm{len}(s)$ is not a multiple of the block size, a certain amount of padding is added to it to make it a multiple, and the hash is generated using what is essentially $s || m || \textrm{padding}$.  Now SHA-1 internally uses 5 registers — it takes in an block, generates new register values, turns the crank, takes in another block, generates new register values, turns the crank ... and so on till the end. When all blocks are exhausted, the register values are concatenated and spit out.  Assume that an attacker knows a certain value of $m$, for which he also knows the hashed key. In such a case, he knows the state of the 5 registers when $(s || m || \textrm{padding}$ was processed. Lets also assume that the attacker knows the length of $s$, so that he can predict how much padding was added.  Here is where I get confused. From what I've read so far, the attack involves taking the known hash, adding a certain amount of padding and then the value that we want. However, isn't the padding already used up in creating the hash? Why are we using padding in our attack? How can I obfuscate (protect) JavaScript? How do I use the Chinese remainder theorem to find all the square roots of 11 in $\mathbb Z_{35}$? How do I create an Ubuntu live USB using a Mac? I'd like to create an Ubuntu live USB stick on a Mac to use to install Ubuntu on another machine. How do I accomplish this?