Unfortunately document viewer only shows me this if I open my PDF document:    If I enter the Adobelink there is no linux version of acrobate reader. I need to open and write some stuff into this document.
I am new to Ubuntu, but I believe I have Ubuntu 11.10 installed correctly.  I am trying to install Acroread using AdbeRdr9.4.6-1_i386linux_enu.deb that I downloaded from the Adobe web site.  How do I do this?
Evaluate the limit      $$ \lim_{n\rightarrow \infty}\left(\frac{n+1}{n}\right)^{n^2}\cdot \frac{1}{e^n} $$   My Attempt:  $$ \lim_{n\rightarrow \infty}\left(\frac{n+1}{n}\right)^{n^2}\cdot \frac{1}{e^n} = \lim_{n\rightarrow \infty}\left(1+\frac{1}{n}\right)^{n^2}\cdot \frac{1}{e^n} $$  How can I solve the problem from this point? How to connect RDS from a different account with allowed IP in AWS? static variables in an inlined function I have a function that is declared and defined in a header file. This is a problem all by itself. When that function is not inlined, every translation unit that uses that header gets a copy of the function, and when they are linked together there are duplicated. I "fixed" that by making the function inline, but I'm afraid that this is a fragile solution because as far as I know, the compiler doesn't guarantee inlining, even when you specify the "inline" keyword. If this is not true, please correct me.  Anyways, the real question is, what happens to static variables inside this function? How many copies do I end up with? can CakePHP automatically create tables from models? Ubuntu 16.04 hangs on splash screen during boot Broken blog link on pages with lists of moderators The page  has a link like this:  which doesn't seem to exist anymore. This is the same on  And also on Prove $| \sum_{i \leq n} \frac{\mu(i)}{i} | \leq 1$ So I am trying to prove the above stated formula. I am completely new to number theory so I thank you in advance for baring with me. I start off by using the definition:  $\frac{\phi(n)}{n} = \sum_{d|n} \frac{\mu(d)}{d}$  Where $\phi$ is Eulers function, and $\mu$ is the Mobius mu function. From here, I use the Mobius inversion formula to give:  $\frac{\mu(n)}{n} = \sum_{d|n}d\frac{\phi(\frac{n}{d})}{n}\mu(d)$  Now summing $n$ up to $x$:  $\sum_{n \leq x}\frac{\mu(n)}{n} = \sum_{n \leq x}\sum_{d|n}d\frac{\phi(\frac{n}{d})}{n}\mu(d)$  Now I'm not fully sure on how I can rearrange things inside the two summations on the right hand side, so leaving things as they are; using that $\sum_{d|n} \mu(d) = 1$, if and only if $n =1$. Hence:  $\sum_{n \leq x}\frac{\mu(n)}{n} = \sum_{d|1}d\phi(\frac{1}{d})\mu(d)$  Thus $d=1$. Subbing this in:  $\sum_{n \leq x}\frac{\mu(n)}{n} = \phi(1) = 1$  I am not sure what I have missed (or done wrong) as to have an equality and not a triangle relation. Any suggestions or ideas would be greatly appreciated I need to calculate the following determinant in order to prove the following equality:  $$\det\begin{pmatrix} a &amp; b &amp; c &amp; d \\ -b &amp; a &amp; -d &amp; c \\ -c &amp; d &amp; a &amp; -b \\ -d &amp; -c &amp; b &amp; a \end{pmatrix} = (a^2+b^2+c^2+d^2)^2.$$  I tried using Gauss-algorithm to get an easier matrix, but I'm not sure if I did it correctly.  Calling the $4$ lines $I$, $II$, $III$ and $IV$, I did:  (1) $II \cdot a$  (2) $III \cdot a$  (3) $IV \cdot a$  After this I did:  (4) $II' + I \cdot b$  (5) $III' + I \cdot c$  (6) $IV' + I \cdot d$  So finally I got the following matrix:  $$\begin{pmatrix} a &amp; b &amp; c &amp; d \\ 0 &amp; a^2+b^2 &amp; bc-ad &amp; ac+bd \\ 0 &amp; ad+bc &amp; a^2+c^2 &amp; cd-ab \\ 0 &amp; bd-ac &amp; ab-cd &amp; a^2+d^2 \end{pmatrix}.$$  I thought this would make the determinant a bit easier, unfortunately I must have done something wrong. Is multiplication with single lines allowed as I have done it?  Thank you very much. Problem: James has a pile of n stones for some positive integer n ≥ 2. At each step, he   chooses one pile of stones and splits it into two smaller piles and writes the product   of the new pile sizes on the board. He repeats this process until every pile is exactly   one stone.      For example, if James has n = 12 stones, he could split that pile into a pile of size   4 and another pile of size 8. James would then write the number 4 · 8 = 32 on the   board. He then decides to split the pile of 4 stones into a pile with 1 stone and a   pile with 3 stones and writes 1 · 3 = 3 on the board. He continues this way until he   has 12 piles with one stone each.      Prove that no matter how James splits the piles (starting with a single pile of n   stones), the sum of the numbers on the blackboard at the end of the procedure is   always the same.   Hint: First figure out what the formula for the final sum will be. Then prove it using strong induction.  The formula I came up with is $n(n-1) / $2. It could be totally wrong...  My (Partial) Solution:  1) Base Case: (n=2) James has one pile of 2 stones. Suppose he takes the top-most stone and puts in one pile A, which now has size 1. He takes the remaining stone and places it into another pile B, which now has size 1. Then the product of the sizes is 1. The sum of all the products on his board is 1. Now, if he were to start again, and take the bottom stone first and put it in pile A, he has a pile of size 1, and then takes the top stone and puts it in pile B, he has a pile of size 1, and the product is 1, with sum of all products on the board is 1.   2) Inductive Hypothesis (Strong Induction): Suppose for some $k \geq 2$, $n$ stones can be split in $ 2 \leq n \leq k $ stones and $k-n$ stones.  3) Inductive Step:  Consider $n=k+1$. What do I do now? Why does cold metal seem colder than cold air? (I apologize for this elementary question. I don't know much about physics.)  Let's say that I put a metal pot in the refrigerator for several hours.  At this point, I guess, the pot and the air (in the refrigerator) have the same temperature.  Now, I touch this pot. It feels very cold. But when I "touch" the air (that is inside the fridge) it doesn't "feel" as cold. I don't feel the same "ouch!" that I feel when I touch the pot.  Why is that? Why does the metal seem colder than air although they both have the same temperature?  (I know that gas has less particles in it in one unit of volume compared to solids and liquids, but since "temperature" means "the average kinetic energy", these fewer air particles are supposed to hit my hand in a velocity that's going to compensate for their lower number, aren't they?)  A related question, for clarification:  If I use a thermometer to measure the temperature of the pot &amp; air (let's assume it's a thermometer that has a probe that can touch objects), will it show the same reading for both? If so, what makes the thermometer different than my hand? I mean, my hand is sort of a thermometer, so why would it fail whereas a non-human thermometer would work? How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime I have the following question where I need to provide a counterexample     if $n$ is prime, then $2^n -1$ is prime   The statement is invalid and I now that $2^n -1$ is not prime when $ n = 11$, but other than plugging in prime numbers is there any other way to figure out whether $2^n -1$ is prime if $n$ is prime? Blender for Chromebook How would I be able to run Blender on a Chromebook? The Rollapp is a farce that demands money for free software, and the whole reason I didn't buy a windows laptop is because I hate Windows 10, so is there another option? Will wolves attack and kill ocelots in Minecraft? I know they kill sheep. I just don't want my cats being eaten. It seems to me, perhaps naïvely, that Aristotle resolved  well, when he said that,      Time is not composed of indivisible nows any more than any other magnitude is composed of indivisibles,    and that Aquinas clarified the matter for the (relatively) modern reader when he wrote      Instants are not parts of time, for time is not made up of instants any more than a magnitude is made of points, as we have already proved. Hence it does not follow that a thing is not in motion in a given time, just because it is not in motion in any instant of that time.     For me, any further attempts at explanation and resolution, such as Russell's, (bar rather tenuous appeals to connections with quantum physics) simply reiterate, and rather labour Aristotle's initial erudite explanation.  What serious arguments exist that counter Aristotle's objection, if any, and why is Aristotle's objection not considered a resolution to this paradox? Why can't I log into minecraft with a mojang account? I have searched the web a lot and could not find an answer that fits my situation. Here are two links that are quite contradictory:       My situation:  I've visited Portugal in December 2012 for 29 days on a Schengen visa valid from December 1st, 2012 to February 1st, 2013 for research purposes (I am a Ph.D. student). I want to visit Sweden from February 10th, 2013 to May 10th, 2013 (89 days). I have applied for a Schengen visa again (for research). How will the 90/180 rule work in my situation? How to find architecture of my PC and Ubuntu? Lualatex and bm package I've updated my latex packages yesterday and have now issues with lualatex. One problem arising for me now is, that lualatex does not print bold characters using the bm package.  When I compile the following MWE with pdflatex everything looks okay, but for lualatex it doesn't:  \documentclass{article} \usepackage{bm} \begin{document} % Bold $\bm{E}$ \\ Normal $E$ % \end{document}   Output using pdflatex    using lualatex    Also trying to fall back to an earlier version of lualatex by using \RequirePackage{luatex85} does not work for me.  When having a look at the log file, there are the suspicious messages   LaTeX Font Info:    Redeclaring math alphabet \mathbf on input line 142. LaTeX Info: Redefining \bm on input line 208. [...] Missing character: There is no х (U+0445) in font cmmi10!   Can anyone tell me, what is going on here and what I need to do to solve this problem, since I am quite sure lualatex and bm worked before? Is it feasible to transform each variable differently while doing multiple regression Accidentally deleted /etc/fstab file I accidentally deleted my /etc/fstab file by running sudo rm /etc/fstab. Without realising what I'd done, I shut down my Ubuntu OS.  Now I'm not able to boot.    My screen looks like this. In some cases, a purple screen appears. Please give me some solutions.