Explanation of two boxes problem?
If you have two envelopes, and ...
In the sentence:     All the information you need is in these folders.   I would have expected to find:     All the information that/which you need is in these folders.   Why are those omitted? Find $\lim\limits_{n \to \infty} \frac{\sqrt 1 + \sqrt 2 + \dots + \sqrt{n}}{n\sqrt{n}}$. $$\lim_{n \to \infty} \dfrac{\sqrt 1 + \sqrt 2 + \dots + \sqrt{n}}{n\sqrt{n}}$$   $$\lim_{n \to \infty} \dfrac{\sqrt 1 + \sqrt 2 + \dots + \sqrt{n}}{n\sqrt{n}} =\lim_{n\to \infty} \dfrac1{n}\sum^{n}_{k = 1} \sqrt{\dfrac k n} $$  While searching this question I found, .   Like in the accepted answer I first compared my series to LRAM,    $$\int_a^b f(x)\,dx=\lim_{n\to\infty}\frac 1n\sum_{i=1}^n f\left(a+\frac{b-a}n i \right)$$  I got $a = 0$, $b = 1$ and $f(x) =\sqrt{x}$ so,  $$\int_0^1 \sqrt{x}\ dx = \dfrac2 3$$ should be the answer.  Is there any simpler method to do this sum ? I have not learnt this method to do infinite sums so I can't use it. How to change file encoding in NetBeans? Laptop power supplies, does current matter? I have two laptops (same manufacture), with the same type of power connector.  However, the power supplies/transformers are slightly different.    The output on the first laptop's power supply is 15.6&nbsp;V at 8.0&nbsp;A. The output on the second laptop's power supply is 15.6&nbsp;V at 5&nbsp;A.  Clearly the voltages are the same, but the currents are different. I assume the second laptop's power supply can not be used on the first, because it can't supply enough power to the laptop.   However, can the first laptop's power supply be safely used on the second laptop? Let $ \mathbb R _ { &gt; 0 } $ be the set of positive real numbers. Find all functions $ f : \mathbb R _ { &gt; 0 } \to \mathbb R _ { &gt; 0 } $ such that $$ f \big ( x y + f ( x ) \big) = f \big( f ( x ) f ( y ) \big) + x $$ for all positive real numbers $ x $ and $ y $.  What I thought: We could change $ x $ by $ y $, and then subtract. Source: Brazil National Olympiad 2019 #3 I am unable to figure out simple solution to add "Bookman Old Style"  as a main font in my latex document. I have used below line but does not give me required font.  \usepackage{bookman}   Could not find any Simple correct answer for this. Pl. suggest how to do it.  I am using windows, pdflatex.  thank you RegEx for Javascript to allow only alphanumeric tmux: enable mouse only when shift pressed What is the exact reason that normal matter can not exist within an event horizon?  I can understand how a super-dense object like a neutron star could accrete mass until its physical radius is less than its Schwarzschild radius and an event horizon forms around it.   But why can't the neutron star remain inside the event horizon as it was before the event horizon formed? Aside from the escape velocity at the surface reaching $c$, what actually changed?  Why must all matter within an event horizon undergo complete physical collapse to a point? I need the cs_CZ.ISO8859-2 locale to exist on Ubuntu 12.04 so a specific unit test can pass. The test makes the following call:  std::locale("cs_CZ.ISO8859-2")   On my OS X Lion install, this locale does exist, so the call to std::locale should work:  $ locale -a | grep cs cs_CZ cs_CZ.ISO8859-2 cs_CZ.UTF-8 $   However, on my Ubuntu 12.04 install, there is only a UTF8 variant, and no ISO8859-2 version of the cs_CZ locale, despite having installed language-pack-cs:  $ dpkg -l | grep language-pack-cs ii  language-pack-cs                       1:12.04+20120417                        translation updates for language Czech ii  language-pack-cs-base                  1:12.04+20120417                        translations for language Czech $ locale -a | grep cs_ cs_CZ.utf8 $   The unit test fails on this machine. Running the unit test under strace shows that it really is looking for the ISO8859-2 variant and not finding it anywhere:  open("/usr/lib/locale/cs_CZ.ISO8859-2/LC_CTYPE", O_RDONLY|O_CLOEXEC) = -1 ENOENT (No such file or directory) open("/usr/lib/locale/cs_CZ.iso88592/LC_CTYPE", O_RDONLY|O_CLOEXEC) = -1 ENOENT (No such file or directory) open("/usr/lib/locale/cs_CZ/LC_CTYPE", O_RDONLY|O_CLOEXEC) = -1 ENOENT (No such file or directory) open("/usr/lib/locale/cs.ISO8859-2/LC_CTYPE", O_RDONLY|O_CLOEXEC) = -1 ENOENT (No such file or directory) open("/usr/lib/locale/cs.iso88592/LC_CTYPE", O_RDONLY|O_CLOEXEC) = -1 ENOENT (No such file or directory) open("/usr/lib/locale/cs/LC_CTYPE", O_RDONLY|O_CLOEXEC) = -1 ENOENT (No such file or directory) open("/usr/share/locale-langpack/cs_CZ.ISO8859-2/LC_CTYPE", O_RDONLY|O_CLOEXEC) = -1 ENOENT (No such file or directory) open("/usr/share/locale-langpack/cs_CZ.iso88592/LC_CTYPE", O_RDONLY|O_CLOEXEC) = -1 ENOENT (No such file or directory) open("/usr/share/locale-langpack/cs_CZ/LC_CTYPE", O_RDONLY|O_CLOEXEC) = -1 ENOENT (No such file or directory) open("/usr/share/locale-langpack/cs.ISO8859-2/LC_CTYPE", O_RDONLY|O_CLOEXEC) = -1 ENOENT (No such file or directory) open("/usr/share/locale-langpack/cs.iso88592/LC_CTYPE", O_RDONLY|O_CLOEXEC) = -1 ENOENT (No such file or directory) open("/usr/share/locale-langpack/cs/LC_CTYPE", O_RDONLY|O_CLOEXEC) = -1 ENOENT (No such file or directory)   I know absolutely nothing about locales, i18n, etc. However, I would like to get this test passing, and changing the test is not an option. If anyone can offer any insight into how to make this locale exist on Ubuntu 12.04 I would appreciate it greatly. Why did the TIE fighter in The Force Awakens have life support? Proof that $\cos(\pi/3)=1/2$ Is it possible to prove that $\cos(\pi/3)=1/2$ without using any trigonometric identities?  To be specific, my calculus-book simply states that with an angle of $\pi/3$ on the unit-circle the points (0,0) and (1,0) are the vertices of an equilateral triangle with edge length 1. But how can one reach such conclusion?  Thanks! When can a hyphen ("-") be used, and what does it mean? I've seen the hyphen (-) used in phrases a lot, for example:     audience-knowing      moves-sometimes      do-gooder   When and why is the hyphen used, and what does it mean when it's used? Registered Apple Developer Agreement when under 18 What is the current state of apple device (iPhone, iPod, etc.) support? What ubuntu applications provide support? (guides, how to's, status) Also, specifically, details on support for syncing music to iPhone's and iPod's with the latest OS version:   Can you sync music to apple devices using >iOS4? (iPhone &amp; iPod) What applications allow you to do this and how? (guides, how to's, status)    What has already been established is:   Apple does not support Linux and has no plans to.  provides some support, however it currently does not support music/video synchronization with devices &gt;iOS4. Go to  and scroll to the section titled "" to see if your device version is supported. Powering NiChrome wire from battery I'm looking to power nichrome wire from battery. The problem I ran into is that desired length/width of the wire has very small resistance ~ 8 Ohm.  Several kinds of batteries I've tested have internal resistance much higher then that, which leads to wire staying cold and battery getting hot.  Is there any way to increase current drawn from the battery? Some kind of amplifier maybe?  Edit:    1.2V(rechargable) and 1.5V one, while not getting hot itself did not provide enough power to heat the wire. 3V did not provide enough power, even stacking 3 of them in series, only provided about 1V of voltage on the wire, and not enough amperage to heat the wire. 9V battery did provide enough amperage to heat the wire, but at the same time got very hot very quickly itself.   PS. I was wondering if  might work for this purpose? How can I easily share links or text between my Android phone and my laptop? Setting chain length My chain broke and in a moment of silliness (I was cold wet and slightly annoyed)  I threw the broken one away before thinking about measuring the new one.  Is there a guide to getting the chain length/tension correct ?  It's an 8 speed road bike (Shimano Sora back, double ring front) Why is it that Android still can't be installed as regular OS? How do you make an image emission without washing out the image? I am trying to make a computer monitor. This means I have to have an image texture for the screen. My image texture is currently connected to an Emission BSDF shader. Unfortunately, when the emission is bright enough to emit light, the image is white-washed. I tried adding a Brightness/contrast node to the image before pushing it into the Emission BSDF, but it seems to directly counter the Emission's strength.  The desired light level   The desired image brightness