Change the word "Appendices" in TOC to "Bijlagen"
Appendix in LaTeX
Induction: Prove that $4^{n+1}+5^{2 n - 1}$ is divisible by 21 for all $n \geq 1$. Induction: Prove that $4^{n+1}+5^{2 n - 1}$ is divisible by 21 for all $n \geq 1$. Excel multiple FIND formula Why do we age? or Do we have a theory of senescence? There seem to be a number of ideas about why we age. Hypotheses include the gradual accumulation of cell metabolic products affecting organism function and the reduction of  during cell division. My hand-wavey idea would be "wear and tear".  Are we anywhere near a consensus theory of senescence? My laptop is filled with viruses and Windows XP is just becoming impossible to work with.   I've been interested in Ubuntu for a while, so, would I be able to use something like Debian to clear my HDD and OS and then install Ubuntu and start fresh? How can they see Harry's invisibility cloak when they are not wearing it? Show that $U_n:=\left(1+\dfrac{1}{n}\right)^n$, $n\in\Bbb N$, defines a monotonically increasing sequence.   I must show that $U_{n+1}-U_n\geq0$, i.e. $$\left(1+\dfrac{1}{n+1}\right)^{n+1}-\left(1+\dfrac{1}{n}\right)^n\geq0.$$  I am trying to go ahead of this step. Cannot replace a packed image in the uv image editor I was trying to replace an image in my UV image editor, but the image defaults to a different image. how do I fix this? Changing Vim indentation behavior by file type Could someone explain to me in simple terms the easiest way to change the indentation behavior of Vim based on the file type? For instance, if I open a Python file it should indent with 2 spaces, but if I open a Powershell script it should use 4 spaces. C non-blocking keyboard input Let $(a_k)$ be a sequence of real numbers and let $b_k=\frac{a_1+a_2+\dots a_k}{k}$ for each $k\in \mathbb{N}$.  Prove that if $(a_k)$ converges to $\alpha\in \mathbb{R}$, then the sequence $(b_k)$ also converges to $\alpha$.  My answer: Let $\epsilon &gt; 0$. Since ($a_k$) converges to $\alpha$, then there exists a $N_{\epsilon1}\in\mathbb{N}$ such that $|a_k - \alpha | &lt; \frac{\epsilon}{2}$ for all $k \geq N_{\epsilon1}$. Notice that $\frac{a_1+...+a_n - n\alpha}{k}$ converges to $0$ as $k$ approaches infinity. Thus, there exists $N_{\epsilon2}\in\mathbb{N}$ such that $|\frac{a_1+...+a_n - n\alpha}{k}|&lt;\frac{\epsilon}{2}$ for all $k&gt;N_{\epsilon2}$. Now, let $N= $max$ (N_{\epsilon1},N_{\epsilon2})$. Then for any $k&gt;N$ we get,  $$\begin{array}{rcll} |b_k-\alpha| &amp;=&amp; |b_k - \alpha*1|&amp;\\ &amp;=&amp; |\frac{a_1+...+a_k}{k} - \frac{k\alpha}{k}|&amp;\\ &amp;=&amp; |\frac{a_1+...+a_n}{k} + \frac{[a(n+1)+...+a_k]}{k} - \frac{(k-n)\alpha}{k} - \frac{n\alpha}{k}|&amp; \text{(notice that $N_{\epsilon1}\leq N&lt;k$)}\\ &amp;=&amp; |\frac{a_1+...+a_n - n\alpha}{k} + \frac{[a(n+1)+...+a_k - (k-n)\alpha]}{k}|&amp;\\ &amp;=&amp; |\frac{a_1+...+a_n - n\alpha}{k} + \frac{[(a(n+1) -\alpha) + ... + (a_k - \alpha)]}{k}|&amp;\\ &amp;=&amp; |\frac{a_1+...+a_n - n\alpha}{k} + \frac{(a(n+1) -\alpha)}{k} + ... + \frac{(a_k - \alpha)}{k}|&amp;\\ &amp;\leq&amp; |\frac{a_1+...+a_n - n\alpha}{k}| + |\frac{(a(n+1) - \alpha)}{k}| + ... + |\frac{(a_k - \alpha)}{k}|&amp; \text{(by the triangle inequality)}\\ &amp;=&amp;|\frac{a_1+...+a_n - n\alpha}{k}| + \frac{|(n+1) - \alpha|}{k} + ... + \frac{|a_k - \alpha|}{k}&amp;\\ &amp;&lt;&amp; \frac{\epsilon}{2} + [\frac{\epsilon}{2}/k + ... + \frac{\epsilon}{2}/k]&amp; \\ &amp;=&amp; \frac{\epsilon}{2} + \frac{\epsilon}{2}*\frac{(k-n)}{k}&amp;\\ &amp;&lt;&amp; \frac{\epsilon}{2} + \frac{\epsilon}{2}&amp; \text{(since $k-n&lt;k$)}\\ &amp;=&amp; \epsilon&amp; \end{array}$$ And since we found such an $N$ for arbitrary $\alpha$, then $(b_k)$ converges to $\alpha$ by definition.  I'm not sure i kept all my variables straightened out. How does this look and if you have a better idea let me know! When editing a question on , I observed that a link which was not rendered in the post was hyperlinked in the edit preview (see pictures below). I tried reproducing it in the  to see if this also happens when the post is posted for the first time and observed the same. It seems to be a bug after the shift to CommonMark, leading to the different rendering of links on client and server-side. A link following a special character (without any space) is not hyperlinked in the post but is hyperlinked in the preview. A link separated from the special character with a white space appears to have no such problem. (see pictures below and my ). Link not hyperlinked in post  Same link hyperlinked in preview Force NTFS permissions inheritance for newly created files Does anybody know a way to force that all files that get created inside some folder inherit the NTFS permissions of that folder.  The problem is the following:  I have a third party software that is creating PDF files inside a certain folder, but the problem is that those files get created with only the permissions for that user and for the administrators group, the file doesn't inherit the permissions of the folder it is in (Include inheritable permissions... is not marked on the files that get created), which give access to other groups of users also. It appears that there are at least two questions here on Ask Ubuntu that are similar to this, but neither has been answered.       Text files can be valid under multiple encodings simultaneously. I would like to know the exact encoding gedit uses to decode a given file. Can this be done in the recent versions of gedit?  (I'd like to note that I am aware of other tools that can determine the encoding of a given file. However, I want to know the encoding as detected by gedit specifically) How to find (and delete) duplicate files I have a largish music collection and there are some duplicates in there. Is there any way to find duplicate files. At a minimum by doing a hash and seeing if two files have the same hash.  Bonus points for also finding files with the same name apart from the extension - I think I have some songs with both mp3 and ogg format versions.  I'm happy using the command line if that is the easiest way. I had originally coded the program wrongly. Instead of returning the Fibonacci numbers between a range (ie. startNumber 1, endNumber 20 should = only those numbers between 1 &amp; 20), I have written for the program to display all Fibonacci numbers between a range (ie. startNumber 1, endNumber 20 displays = First 20 Fibonacci numbers). I thought I had a sure-fire code. I also do not see why this is happening.  startNumber = int(raw_input("Enter the start number here ")) endNumber = int(raw_input("Enter the end number here "))  def fib(n):     if n &lt; 2:         return n     return fib(n-2) + fib(n-1)  print map(fib, range(startNumber, endNumber))   Someone pointed out in my Part II (which was closed for being a duplicate - ) that I need to pass the startNumber and endNumber through a generator using a while loop. Can someone please point me in the direction on how to do this? Any help is welcome.    I'm a learning programmer and I've run into a bit of a jumble. I am asked to write a program that will compute and display Fibonacci's Sequence by a user inputted start number and end number (ie. startNumber = 20 endNumber = 100 and it will display only the numbers between that range). The trick is to use it inclusively (which I do not know how to do in Python? - I'm assuming this means to use an inclusive range?).  What I have so far is no actual coding but rather:   Write Fib sequence formula to infinite Display startNumber to endNumber only from Fib sequence.   I have no idea where to start and I am asking for ideas or insight into how to write this. I also have tried to write the Fib sequence forumla but I get lost on that as well. UK Standard Visitor visa application to sit for PLAB 1 without savings or job I am a medical doctor in Pakistan. I have been on a career break to allow myself to study full time for the IELTS exam (from which I recently got the required band score) and PLAB 1. I have now registered and paid for the PLAB 1 exam in UK for June 2016, as the next sitting in Pakistan is in November 2016 and I feel like I am ready to do the exam sooner.  Due to having no current employment, my savings are limited (around 25,000 Pakistani Rupees) but I live with my parents and do not have any financial commitments at home.  My savings have depleted in the past ten months whilst I have taken a career break and the money has been used for my own personal expenses. My trip to the UK is being funded by my grandfather who is a British citizen. He is a retired doctor with a good NHS pension. He has provided me with:   6 months bank statements which clearly show his pension deposits   Letter from NHS Pensions stating his pension   Sponsorship letter stating that he will pay for my PLAB exam fee, travel, accommodation and subsistinence costs whilst in the UK   Copy of British passport  Document confirming that he owns the house he lives in mortgage-free Confirmation email from GMC stating he has paid the PLAB exam fee.   Without large personal savings and no current job (but I have job offers now) would my application be rejected or is the strong sponsorship going to be good enough?  Are there any other documents I should consider submitting that may help me get a visa? In the new canon what do we actually know about Darth Plagueis? I read and loved  but with all the recent changes to what is and isn't canon I'm losing track.  There's a common theory that Supreme Leader Snoke is Darth Plagueis, most are discounted because Plagueis is a Muun. But where does that information come from? What current canon information do we have about Plagueis that disproves this theory and what has been marked as Legends? Setup or "set up"? The word setup (as a noun), I feel, has become an acceptable part of the English language, at least insofar as technical manuals or computer textbooks are concerned. However I find that the word is used very often in verb form like so:     "You can setup the program quite easily ..."   when in fact my understanding is that the actual sentence should be:     "You can set up the program quite easily ..."   I would like to know if setup can be used as a verb. The situation seems be very similar to the word output (as a noun). Output is a purely technical word and its use is restricted solely to technical texts or at least in a technical context within non-technical books. However it is also used in verb form now like so:     "The system will output the signal ..."   I would be very grateful if this question is answered. Thank you If I want to investigate how two continuous variables are linked, what is the difference between calculating the correlation coefficient (Pearson's $r$) versus calculating the (simple linear) regression coefficient?  I see people who, if the regression coefficient is significantly different from zero, talk about the two variables as if they are correlated, which is confusing as it suggests that the two coefficients (correlation, regression) are the same thing.  Having said that, isn't $r$ a measure of the (regression line) slope anyway? I'm confused!! BufferedWriter not writing everything to its output file