My answer to a question keeps being posted as comment
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Prove that : $\displaystyle \lim_{n\to \infty} \frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+\cdots+\frac{1}{2n}=\ln 2$    the only thing I could think of is that it can be written like this :  $$ \lim_{n\to \infty} \sum_{k=1}^n \frac{1}{k+n} =\lim_{n\to \infty} \frac{1}{n} \sum_{k=1}^n \frac{1}{\frac{k}{n}+1}=\int_0^1 \frac{1}{x+1} \ \mathrm{d}x=\ln 2$$  is my answer right ? and are there any other method ?(I'm sure there are) How do I close a terminal without saving the history? More than once I've accidentally run a number of commands and polluted my bash history. How do I close my terminal without saving my bash history? I'm using Fedora. How can I mine redstone ore? I found redstone ore in Survival Mode (Minecraft Pocket Edition) and tried to use all five tools to collect it. It took about a minute or two to break, but I couldn't collect anything from it once broken.  How do I mine redstone ore? Showing two ring homomorphisms that agree on the integers must agree on the rationals I have two ring homomorphisms $f,g\colon \mathbb{Q}\to X$. I know that $f=g$ on the integers. How can I show that $f$ and $g$ agree on the rationals?   My attempt:  let $x,y \in \mathbb{Z}$, $y\neq 0$.  $$\begin{align*} f(x/y)&amp;=f(x)f(1/y) &amp;&amp;\text{because }f\text{ is a ring homomorphism}\\  &amp;=g(x)f(1/y) &amp;&amp;\text{because }f\text{ and }g\text{ agree on the integers} \end{align*}$$  I do not know how to rewrite $f(1/y)$ so that I can replace it with $g(1/y)$. Any hints will be much appreciated. Thanks. Why can Arwen decide her mortality? I have been thinking of getting a flash to improve my low light photography (particularly indoors). However, there seem to be a number of different models available at similar price points (budget of INR 8,000-12,000 ~$150-250). What features and functionality should I look for to choose a suitable flash?  I'm using a Canon 550D with the 18-55mm IS &amp; 55-250mm IS lenses. Metz seems to be one of the brands easily available in India (beside the OEM flashes). Currently, I am considering the Metz 36 AF-5, 44 AF-1 and 50 AF-1, which seem to be considerably cheaper than their Canon counterparts. Do not enumerate a section, but add it into table of contents How do I rid of number of a section in the way that it still would be in the table of contents.  If I use   ... \section{SN1} ...   then I see this section name in table of contents as   1 SN1  2 SN2  3 SN3  ...   If I use   \section*{SN}   I don't see it in the content:   1 SN2  2 SN3   How to get in content just   SN1  1 SN2  2 SN3   ? I have a laptop which is connected to the internet with ADSL modem, and I would like to share the internet for any laptop connecting to wireless router from my laptop using hotspot.  This is what I want:  ┌────────────────────┐ │ ADSL modem         │ └───┬────────────────┘     │ ┌───┴───────────────────────┐ │ laptop's wired adaptor    │ │                           │ │ Hotspot software          │ │                           │ │ laptop's wireless adaptor │ └───┬───────────────────────┘     │ ┌───┴──────────────────────┐ │ wireless router(linksys) │ └───┬──────────────────────┘     │ ┌───┴─────────────────────────────┐ │ Laptop computers and cellphones │ └─────────────────────────────────┘   How can I do that? How to export debug logs? I spend my days waiting on the Force.com Console and it makes me crazy, I have a pretty nice machine and it still chokes on the details sometimes.  Anyways, I saw  had given a  and is presenting again this year Dreamforce '12.  However, it seems like they're presentation is targeted at using their product, or for that matter others like it (, ) on Heroku, and not really targeting APEX/VisualForce development!  Is this the case? Are there any better solutions out there for reviewing logs?  Are there any APIs that allow you to export your debug logs out of SFDC programatically? Or has anyone even tried to tackle this? Since arrays and hashes can only contain scalars in Perl, why do you have to use the $ to tell the interpreter that the value is a scalar when accessing array or hash elements? In other words, assuming you have an array @myarray and a hash %myhash, why do you need to do:  $x = $myarray[1]; $y = $myhash{'foo'};   instead of just doing :  $x = myarray[1]; $y = myhash{'foo'};   Why are the above ambiguous?   Wouldn't it be illegal Perl code if it was anything but a $ in that place? For example, aren't all of the following illegal in Perl?  @var[0]; @var{'key'}; %var[0]; %var{'key'}; During the next quarter at uni, I'll be taking a course in real analysis and since I prefer studying with an additional text I thought I'd come here to look for some book recommendations.  My background: I'm comfortable with linear algebra and single variable calculus, but shakey on multivariable calculus. I did have a slight introduction in to geometry.  For linear algebra I found the common recommendation of Hoffman &amp; Kunze to be very helpful (although the abstractness came as a bit of a kicker at first).   For Single variable calculus I used the book Calculus by Adams and Essex, which I found frustrating to work with, because it often left me guessing at what they were trying to do or why they were doing it. I also felt that they exercised a certain lack of rigour. (Which may be due to the subject which would make it hard to derive from axioms.)  Details: Though it would be a complementary text, I'd prefer one which will still hold value as a work of reference at a later point in my studies. I've heard that Rudin's Principles of mathematical analysis is one of the better textst out there, but also read several comments discouraging Rudin's book as a first introduction to real analysis, hence my quest to gather more information and maybe get some more personalised recommendations.  The course: The mandatory course literature will consist of lecture notes, but 4 texts are suggested as recommended reading.   T.M. Apostol, Mathematical analysis. Addison-Wesley (1974) J. Dieudonné, Foundations of Modern Analysis. Academic Press (1960) A. van Rooij, Analyse voor Beginners.Epsilon Uitgaven, no. 6 (2003)   R.S. Strichartz, The way of analysis (1995)   Thanks in advance! SEDE should pick up on changes to community metadata It appears that site meta data isn't updated in SEDE. As an example, Moderators.SE was  to  in December 2014. It is still listed in SEDE as Moderators.SE, as of July 2015.  To search for Community Building data, we need to search the "Moderators" community:    It is not listed as Community Building: for loop wget directory creation error As a Ubuntu beginner. I am trying to download links from multiple text files with wget2 in batch. The -P &quot;$f&quot; creates directory name with .txt suffix. Is it possible to ignore .txt for -P &quot;$f&quot;. Any modification suggestions. for f in *.txt;do wget2 -i &quot;$f&quot; -P &quot;$f&quot;;done When I apply to a PhD program, may I ask a postdoc who closely supervised me to write a recommendation letter? My supervisor also has written one for me, but I believe the postdoc can comment on my research skills in a more detailed and precise way. Does a postdoc have enough authority to convince admission committee? "The volume boot has only 0 bytes disk space remaining" After a recent update, I'm getting an alert saying:  The volume boot has only 0 bytes disk space remaining   But my computer has plenty of HD space free. Does anyone know how I resolve this. (If it's relevant, I'm using the whole disk encryption feature of the alternate install image for Ubuntu 12.04). Editing question title creates whole new question and other question list problems pkgloader is not finding l3regex I know the thread  However, there is no Linux anymore in the installation site .  Unsuccessful attempts   I do DriraWassim's proposal which does not add anything to apt-get and does not show the installed .deb package in the path/search  sudo apt-get install libxml2:i386  sudo apt-get update sudo apt-get upgrade  apt-cache search adobereader-enu   I download the newest .deb package  and run it.  I cannot find the application anywhere in the system. It is not in the path and not in Ubuntu's search. How can you start it?   System: Ubuntu 16.04, 64 bit Hardware: Macbook Air 2013-mid Linux kernel: 4.6 I was pondering a bit more about  question regarding being able to &quot;omit&quot; the base case in a proof by strong induction due to vacuous truth. The post states:  Strong induction proves a sequence of statements $P(0), P(1), …$ by proving the implication &quot;If $P(m)$ is true for all nonnegative integers $m$ less than $n$, then $P(n)$ is true.&quot; for every nonnegative integer $n$. There is no need for a separate base case, because the $n=0$ instance of the implication is the base case, vacuously.  However, if we consider $n=0$, we would have that the statement is vacuously true, which I would take to mean that the implication is true regardless of the validity of $P(0)$. However, clearly it's necessary for $P(0)$ to hold for an induction proof to be valid. So I'm confused on how, by omitting the base case, $n=0$ isn't just a tautology, making the implication true regardless of whether $P(0)$ actually holds. Is there an app that will notify me (in notifications center) if a process is using up a high percentage of CPU for a specified amount of time? The other day, I was sitting in a coffee shop working, when I looked down to find that 25% of my battery was left.   I looked at my Activity Monitor and saw that the time machine process was going at 90% for a while (as long as I was watching it).   Are there any apps that can notify me if a process is at a certain level for a certain amount of time?