$(a_n+a_{n+1})$ is convergent implies $(a_n/n)$ converges to $0$
$\lim_{n \rightarrow\infty} ~ x_{n+1} - x_n= c , c > 0$ . Then, is $\{x_n/n\}$ convergent?
How may I reference the script tag that loaded the currently-executing script? How can I reference the script element that loaded the javascript that is currently running?  Here's the situation. I have a "master" script being loaded high in the page, first thing under the HEAD tag.  &lt;!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"  "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"&gt; &lt;html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"&gt; &lt;head&gt; &lt;script type="text/javascript" src="scripts.js"&gt;&lt;/script&gt;   There is a script in "scripts.js" which needs to be able to do on-demand loading of other scripts. The normal method doesn't quite work for me because I need to add new scripts without referencing the HEAD tag, because the HEAD element hasn't finished rendering:  document.getElementsByTagName('head')[0].appendChild(v);   What I want to do is reference the script element that loaded the current script so that I can then append my new dynamically loaded script tags into the DOM after it.  &lt;script type="text/javascript" src="scripts.js"&gt;&lt;/script&gt; loaded by scripts.js--&gt;&lt;script type="text/javascript" src="new_script1.js"&gt;&lt;/script&gt; loaded by scripts.js --&gt;&lt;script type="text/javascript" src="new_script2.js"&gt;&lt;/script&gt; Why does the base of this slinky not fall immediately to gravity? My guess is tension in the springs is a force > mass*gravity but even then it is dumbfounding. I need to do this for displacement mapping, subdivision gives a bad result and makes triangles distinguishable.    Related to:   But I get the error "No other selected object found to use for projection". How should I validate an e-mail address? How to connect two parents to the same child, with parents not in the same tree? I'm trying to draw a specific tree, with two parents node linked to the same child. The problem is that one of the parent is outside the main tree.  Here's the code I have for the moment:  \documentclass{article} \usepackage{tikz-qtree,tikz-qtree-compat} %\usepackage{gb4e} \usepackage{forest}  \begin{document}  %\begin{exe} \begin{forest} qtree edges/.style={for tree= parent anchor=north, child anchor=south}    [A, grow=north        [C, name=C, grow'=north            [D, grow=north ]            [E, name=t5, grow=north ]        ]        [B, grow=north ]    ]    \hspace{0.8cm}    [$F$, name=F, grow=north ]    %\draw (F.north) -- (C.south); \end{forest} %\end{exe}  \end{document}   I'd like the nodes F and C to be connected. I don't know why, but if I delete the dollar signs, node F doesn't even appear on my document.  Another thing is that I want the forest environment to be embedded in an example environment, but this doesn't work either.  Thanks in advance for your help! I deleted a folder in Ubuntu, how can I recover it? The folder is massive (390GB) and contains many different files. The file system is ext4  I was about to copy this file to another hard drive using gksudo nautilus so I didnt have do a massive chmod operation on the destination hard drive, but then I accidentally hit move to trash, which in gksudo nautilus means permanent deletion. I checked the trash but it's not even an operation...  I have seen tools like testdisk and other recovery tools but none that can recover and whole folder because its made up of different files.   I don't think that this would work but if I deleted the partition could I just recover the whole partition at once?  Or would this be wrong because i have already deleted the partition's content? This is my first job in Linux IT.  I don't have a backup... I was trying to make one because the old backup drive died :( Must an ideal contain the kernel for its image to be an ideal? How does one go about and try to find all subclasses of a given class (or all implementors of a given interface) in Java? As of now, I have a method to do this, but I find it quite inefficient (to say the least). The method is:    Get a list of all class names that exist on the class path Load each class and test to see if it is a subclass or implementor of the desired class or interface   In Eclipse, there is a nice feature called the Type Hierarchy that manages to show this quite efficiently. How does one go about and do it programmatically? I understand that the mechanics and design of a lightsaber aren't that complicated.  Do others besides the Jedi and Sith (or their minions) make or use lightsabers?  And if they don't, why not? I've never really understood why math induction is supposed to work.  You have these 3 steps:   Prove true for base case (n=0 or 1 or whatever) Assume true for n=k.  Call this the induction hypothesis. Prove true for n=k+1, somewhere using the induction hypothesis in your proof.   In my experience the proof is usually algebraic, and you just manipulate the problem until you get the induction hypothesis to appear.  If you can do that and it works out, then you say the proof holds.  Here's one I just worked out,  Show $\displaystyle\lim_{x\to\infty} \frac{(\ln x)^n}{x} = 0$  So you go:   Use L'Hospital's rule. $\displaystyle\lim_{x\to\infty} \frac{\ln x}{x} = 0$. Since that's $\displaystyle\lim_{x\to\infty} \frac{1}{x} = 0$. Assume true for $n=k$. $\displaystyle\lim_{x\to\infty} \frac{(\ln x)^k}{x} = 0$. Prove true for $n=k+1$.  You get $\displaystyle\lim_{x\to\infty} \frac{(\ln x)^{k+1}}{x} = 0.$   Use L'Hospital again: $\displaystyle\lim_{x\to\infty} \frac{(k+1)(\ln x)^{k}}{x} = 0$.  Then you see the induction hypothesis appear, and you can say this is equal to $0$.  What I'm not comfortable with is this idea that you can just assume something to be true ($n=k$), then based on that assumption, form a proof for $n=k+1$ case.  I don't see how you can use something you've assumed to be true to prove something else to be true. Are there any good tools besides SeleniumRC that can fetch webpages including content post-painted by JavaScript? What is the difference between electric potential, potential difference (PD), voltage and electromotive force (EMF)? preventDefault() on an  tag ERROR: cuvid requested, but not all dependencies are satisfied: cuda/ffnvcodec I am trying to compile FFMPEG with Nvidia Cuda support, on Debian 9.3. Parameters, what I am using:  --enable-cuda --enable-cuvid --enable-nvenc --extra-cflags=-I/usr/local/cuda/include --extra-ldflags=-L/usr/local/cuda/lib64 --enable-gpl --enable-libx264 --disable-x86asm --enable-libx265 --enable-libfdk-aac --enable-nonfree   Nvidia Cuda with drivers are installed. When I try to configure ffmpeg, it says:  ERROR: cuvid requested, but not all dependencies are satisfied: cuda   Newer ffmpeg will show a similar, re-worded message:  ERROR: cuda requested, but not all dependencies are satisfied: ffnvcodec   I absolutely don't know why I'm having this issue, because I am compiling ffmpeg on all of our trans-coding servers. How to manage users and groups using GUI? Just switched from 10.04 to 11.10. I'm wondering about the limited options in the GUI for managing users and groups. Where is the old GUI to change groups, id's, etc. I know that I can do this from cli, that's no problem. But I want this comfortable GUI back. Use of pizza stone in gas oven I have a new gas kitchen stove.  The oven seems to burn so easily. I have a thermometer in there and it is registering the temp that I have the oven set on.  I have seen where people have used a pizza stone to even out the heat.  I want to know if you place a rectangle pizza stone directly on the bottom of the oven or should it be placed on a rack on the lowest setting?  I would appreciate replies from anyone who has used this and if it had helped the problem I am currently trying to establish a clear picture of pure/mixed/entangled/separable/superposed states. In the following I will always assume a basis of $|1\rangle$ and $|0\rangle$ for my quantum systems. This is what I have so far:   superposed: A superposition of two states which a system $A$ can occupy, so $\frac{1}{\sqrt{2}}(|0\rangle_A+|1\rangle_A)$ seperable: $|1\rangle_A|0\rangle_B$ A state is called separable, if its an element of the (tensor)product basis of system $A$ and $B$ (for all possible choices of bases) entangled: $\frac{1}{\sqrt{2}}(|0\rangle_A|1\rangle_B+|1\rangle_A|0\rangle_B)$ is not a state within the product basis (again for all possible bases). mixed state: Is a statistical mixture, so for instance $|1\rangle$ with probability $1/2$ and $|0\rangle$ with probability $1/2$ pure state: Not a mixed state, no statistical mixture   I hope that the above examples and classifications are correct. If not it would be great if you could correct me. Or add further cases, if this list is incomplete.   On wikipedia I read about      Another way to say this is that while the von Neumann entropy of the whole state is zero (as it is for any pure state), the entropy of the subsystems is greater than zero.   which is perfectly fine. However I also read on wikipedia a criterion for :     Another, equivalent, criterion is that the von Neumann entropy is 0 for a pure state, and strictly positive for a mixed state.   So does this imply that if I look at the subsystems of an entangled state, that they are in a mixed state? Sounds strange... What would be the statistical mixture in that case?  Moreover I also wanted to ask, whether you had further illustrative examples for the different states I tried to describe above. Or any dangerous cases, where one might think a state of one kind to be the other? I have a JavaScript object. Is there a built-in or accepted best practice way to get the length of this object? const myObject = new Object(); myObject[&quot;firstname&quot;] = &quot;Gareth&quot;; myObject[&quot;lastname&quot;] = &quot;Simpson&quot;; myObject[&quot;age&quot;] = 21; Do mankind and manmade activities/constructions have any effect on the rotation of the Earth? Numbered list in rows in tables I want to have numbered listing in each row, I've tried with \rownumber, but it doesn't work. I wrote a number at the beginning, but Could it be automatically?  Can you help me? This is my code:  \documentclass[10pt, a4paper]{article}  \usepackage{fontspec} \setmainfont{Arial}  \usepackage{color, colortbl} \definecolor{Gray}{gray}{0.9}  \begin{document}  \begin{table}[h!] \tiny \begin{tabular}{|&gt;{\raggedright\arraybackslash}m{30mm}|&gt; {\raggedright\arraybackslash}m{5mm}|&gt;{\raggedright\arraybackslash}m{5mm}|&gt;{\raggedright\arraybackslash}m{5mm}|&gt;{\raggedright\arraybackslash}m{5mm}|&gt;{\raggedright\arraybackslash}m{5mm}|&gt;{\raggedright\arraybackslash}m{5mm}|&gt;{\raggedright\arraybackslash}m{5mm}|&gt;{\raggedright\arraybackslash}m{5mm}|&gt;{\raggedright\arraybackslash}m{5mm}|&gt;{\raggedright\arraybackslash}m{5mm}|&gt;{\raggedright\arraybackslash}m{5mm}|&gt;{\raggedright\arraybackslash}m{5mm}|} \hline \multicolumn{1}{|&gt;{\centering\arraybackslash}m{30mm}|}{\rowcolor{Gray}\textbf{Text}} &amp; \multicolumn{1}{|&gt;{\centering\arraybackslash}m{5mm}|}{\textbf{Sem 1}} &amp; \multicolumn{1}{|&gt;{\centering\arraybackslash}m{5mm}|}{\textbf{Sem 2}} &amp; \multicolumn{1}{|&gt;{\centering\arraybackslash}m{5mm}|}{\textbf{Sem 3}} &amp; \multicolumn{1}{|&gt;{\centering\arraybackslash}m{5mm}|}{\textbf{Sem 4}} &amp; \multicolumn{1}{|&gt;{\centering\arraybackslash}m{5mm}|}{\textbf{Sem 5}} &amp; \multicolumn{1}{|&gt;{\centering\arraybackslash}m{5mm}|}{\textbf{Sem 6}} &amp; \multicolumn{1}{|&gt;{\centering\arraybackslash}m{5mm}|}{\textbf{Sem 7}} &amp; \multicolumn{1}{|&gt;{\centering\arraybackslash}m{5mm}|}{\textbf{Sem 8}} &amp; \multicolumn{1}{|&gt;{\centering\arraybackslash}m{5mm}|}{\textbf{Sem 9}} &amp; \multicolumn{1}{|&gt;{\centering\arraybackslash}m{5mm}|}{\textbf{Sem 10}} &amp; \multicolumn{1}{|&gt;{\centering\arraybackslash}m{5mm}|}{\textbf{Sem 11}} &amp; \multicolumn{1}{|&gt;{\centering\arraybackslash}m{5mm}|}{\textbf{Sem 12}}\\ \hline 1. Text text text text text text text text text text text text text &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;\\\hline 2. Text text text text text text text text text text text text text &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;\\\hline 3. Text text text text text text text text text text text text text  &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;\\\hline 4. Text text text text text text text text text text text text text &amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;\\\hline  \hline \end{tabular} \end{table}  \end{document}