How do I set the world spawn in minecraft? 1.12.1
How to set spawnpoint?
Exam with 18pt main font Evaluating the sum after reordering an infinite series $1-\frac {1} {2}+\frac {1} {3}-\frac {1} {4}+\ldots $ If in the series  $1-\dfrac {1} {2}+\dfrac {1} {3}-\dfrac {1} {4}+\ldots $ the order of the terms be altered, so that the ratio of the number of positive terms to the number of negative terms in the first $n$ terms is ultimately $a^{2}$, show that the sum of the series will become $\log \left( 2a\right) $.  Solution attempt. Let $p$ be the number of positive terms in the first $n$ terms of the reordered series so based on the question we are allowed $a^{2}=\dfrac {p} {n-p}$. Now solving for p we get $p=\dfrac {a^{2}n} {\left( 1+a^{2}\right) }$ and $n-p=\dfrac {n } {\left( 1+a^{2}\right) }$.  We also observe that in the original series only the odd terms are positive and only the even terms are negative.  Let's define $S_{odd}=1+\dfrac {1} {3}+\dfrac {1} {5}+.\ldots +\dfrac {1} {2n-1}$ and $S_{even}=\dfrac {-1} {2}\dfrac {-1} {4}\ldots -\dfrac {1} {2n}$  $S_{Reordered}=S_{odd_{p}}+S_{even_{n-p}}$  $S_{Reordered}=\sum _{t=1}^{t=P}\dfrac {1} {2t-1}+\sum _{t=1}^{t=(n-P)}\dfrac {-1} {2t}$ $S_{Reordered}=\sum _{t=1}^{t=\dfrac {a^{2}n} {\left( 1+a^{2}\right) }}\dfrac {1} {2t-1}+\sum _{t=1}^{t=\dfrac {n } {\left( 1+a^{2}\right) }}\dfrac {-1} {2t}$    In order to extend $S_{Reordered}$ from n terms to an infinite length. I guess i should take the limit of the $S_{Reordered}$ as $n\rightarrow \infty $ which would make the upper values of $t$ (Not sure of technical term here) to be $\infty$ giving me   $S_{Reordered}=\sum _{t=1}^{t=\infty}\dfrac {1} {2t-1}+\sum _{t=1}^{t=\infty}\dfrac {-1} {2t}$   and i have lost the $a$ from the expression. I guess i am stuck i need to perform some step to capture a before taking the limit. Any help would be much appreciated. I want to find the interval of convergence of $$\sum_{n=0}^\infty (\frac{n}{n+1})^{n^2}(2x)^n$$ By the root test, $\sqrt[n]{|(\frac{n}{n+1})^{n^2}(2x)^n|}=|(\frac{n}{n+1})^{n}(2x)|$  And $(\frac{n}{n+1})^n=(1-\frac{1}{n+1})^n\to\frac1e$ as $n\to\infty$  So I've got an open interval(of convergence) s.t. $|\frac1e 2x|&lt;1\implies |x|&lt;\frac e2$.  Now I need to figure out whether the series is convergent or not at the end points, $x=\frac e2, -\frac e2$.  So there are two series I need to deal with, namely, $\sum_{n=0}^\infty (\frac{n}{n+1})^{n^2}e^n$ and $\sum_{n=0}^\infty (\frac{n}{n+1})^{n^2}(-1)^ne^n$.  Suppose $(\frac{n}{n+1})^{n^2}$ is increasing. Then $$(\frac{n}{n+1})^{n^2}&lt;(\frac{n+1}{n+2})^{(n+1)^2}\iff 1&lt;(\frac{n+1}{n+2})^{(n+1)^2}(\frac{n+1}{n})^{n^2}$$ $$\iff 1&lt;(1-\frac{1}{n+2})^{2n+1}(1+\frac{1}{n^2+2n})^{n^2}$$  But $(1-\frac{1}{n+2})^{2n+1}\to\frac{1}{e^2}$ and $(1+\frac{1}{n^2+2n})^{n^2}&lt;(1+\frac{1}{n^2})^{n^2}\to e$  So I have $1&lt;\frac1e&lt;1$, which is a contradiction. Hence $(\frac{n}{n+1})^{n^2}$ is not increasing. But I don't know if it's decreasing. (is it true that $(1+\frac{1}{n^2+2n})^{n^2}\to e$?)  If $(1+\frac{1}{n^2+2n})^{n^2}\to e$ is true, then $(\frac{n}{n+1})^{n^2}e^n$ converges to some positive number, so $\sum(\frac{n}{n+1})^{n^2}e^n$ diverges. But I don't know if it's decreasing: can't apply the alternating series convergence test(Leibniz's criterion).  So, can you help me with the two end points? On every boot up I get this:    For about 10 seconds (or more) before the "normal" Ubuntu Gnome loading screen and the login screen comes up.  I've read some questions and a bug report about this already, but this problem was dismissed as a minor inconvenience or there were no real solutions (that worked for me). For me, this problem leads to an unacceptable slow boot compared to Ubuntu (Unity) or Windows.  Does anybody know how to fix this or is this a "feature" of Ubuntu Gnome and not a bug? I already know that if groups $G,H,K$ are finitely generated abelian groups, following is true.  If $G\times K$ is isomorphic to $H\times K$, then $G$ is isomorphic to $H$. I prove this by uniquness of factorization of finitely generated abelian groups.  My questions are   If group $G$ is finite,$G\times K$ is isomorphic to $H\times K$, then $G$ is isomorphic to $H$? Can you give me a easiest proof and it can be proved by projection function on external direct product? If $G,H,K$ are groups.  If $G\times K$ is isomorphic to $H\times K$, then $G$ is isomorphic to $H$. This statement is false. What is a counterexample?   *$\times$ is external direct product Show that $\sqrt{n^2+1}-n$ converges to 0 I want to use the definition of the limit to show that $\sqrt{n^2+1}-n$ converges to 0.  The definition is as follows: if $\sqrt{n^2+1}-n$ converges to 0, then $\forall \epsilon&gt;0$, there exists an $N&gt;0$ such that $n\ge N \implies \mid\sqrt{n^2+1}-n\mid&lt;\epsilon$.  Now I want to start backwords in order to figure out how to pick N. I know:   $\mid\sqrt{n^2+1}-n\mid=\sqrt{n^2+1}-n$   since $n$ is a natural number and $\sqrt{n^2+1}&gt;n$. So I need to pick an N such that $\sqrt{n^2+1}-n&lt;\epsilon$. I tried multiplying $\sqrt{n^2+1}-n$ by $\frac{\sqrt{n^2+1}+n}{\sqrt{n^2+1}+n}$ but that didn't really seem to help.   Do you have any ideas on how to find this N?  Thanks How to highlight important parts (with a gray background) In the below link        the author highlights anything which is important using a greyish color background. For example, if you see Equation 1.5.3 (which on page 22 of the book) it is highlighted in grey. I would like to know the TeX commands for producing similar output. With Ubuntu 16.04 laptop doesn't suspend when lid is closed I have a Dell 7737 laptop, and with Ubuntu 16.04 it no longer suspends when the laptop lid is closed. With 14.04 closing the lid put the laptop to suspend as expected. However, I reloaded the system with Ubuntu 16.04 and now closing the laptop does nothing. The laptop continues to run as if nothing happened.  When I manually select "Suspend" from the menu it works as expected. (Though it does prompt me to double login on resume. No, not encryption login followed by OS login. This is a double OS login.)  NOTE: Altering the System Settings|Power doesn't seem to affect anything.  Any ideas on what changed from 14.04 to 16.04 in this area? How do I become a Werewolf? I've heard that one of (maybe the only?) secret races in this game is a werewolf.  How do I become a werewolf?  And by extension, how do I cure lycanthropy, that is, if there even is a cure? Project point onto line in Latitude/Longitude Given line AB made from two Latitude/Longitude co-ordinates, and point C, how can I calculate the position of D, which is C projected onto D.  Diagram: What exactly is weakly informative prior? Is there a precise definition of weakly informative prior?  How is it different from a subjective prior with broad support? Problems with partial derivatives. I have created a 'control' using jQuery and used jQuery.extend to assist in making it as OO as possible.  During the initialisation of my control I wire up various click events like so  jQuery('#available input',              this.controlDiv).bind('click', this, this.availableCategoryClick);   Notice that I am pasing 'this' as the data argument in the bind method. I do this so that I can get at data attached to the control instance rather from the element that fires the click event.   This works perfectly, however i suspect there is a better way  Having used Prototype in the past, I remember a bind syntax that allowed you to control what the value of 'this' was in the event.  What is the jQuery way? terminal: non-english characters I used to be able to copy&amp;paste (or type if I load respective keyboard layout) any kind of characters (eg. é ö ñ ß و 好) in my console/terminal.  Now I bought a new computer and it does not work any more, only English/ASCII characters (but in other programs, e.g. firefox, it still works).  Distribution: Ubuntu. Terminals tried: gnome-terminal, xterm, konsole.  I tried  but after reboot echo $LANG still gives C. I also tried setting Character encoding to Unicode(UTF-8) in the gnome-terminal Terminal-menu - without effect.  Question: How can I get a terminal that is able to deal with non-English characters? Story where vampires are created by drop absorbed on neck? I have been trying to identify a book that I read maybe 25-30 years ago (1987-1992), in which there are vampire or vampire-like creatures, but instead of being created in the traditional way (e.g. bite on the neck), something drops a drop of a fluid on the back of their neck, which is then absorbed into the body and transforms them. I have a vague notion that some sort of tree is what creates these drops. The drops may have had a shiny metallic appearance.  I've tried to find this book before and always came up short. I'm starting to think the whole thing was a dream and I never read it at all. But I really feel like it was a book or at least a short story. Some guy called one of my Snipplr submissions "crap" because I used if ($_SERVER['REQUEST_METHOD'] == 'POST') instead of if ($_POST)  Checking the request method seems more correct to me because that's what I really want to do. Is there some operational difference between the two or is this just a code clarity issue? Why is this regex allowing a caret? Prove any orthogonal 2-by-2 can be written in one of these forms.... I'd like to prove that any orthogonal $2 \times 2$ matrix can be written   $$\bigg(\begin{matrix}    \cos x &amp; -\sin x  \\     \sin x &amp; \cos x   \end{matrix}\bigg) \hspace{1.0em} \text{or} \hspace{1.0em} \bigg(\begin{matrix}    \cos x &amp; \sin x \\    \sin x &amp; -\cos x \end{matrix}\bigg)$$  for $0 \le x &lt; 2\pi$.  I have no idea how to do this. I feel like this is something I've missed and is really straightforward but I can't find it in my book... What is the easiest way to resolve apt-get BADSIG GPG errors? I frequently cross this issue, and always have to google for an answer. Does anyone have a permanent fix for BADSIG errors from apt-get?     W: GPG error:    lucid   Release: The following signatures were   invalid: BADSIG 54422A4B98AB5139   Oracle Corporation (VirtualBox archive   signing key) Why do backgrounded processes sometimes stop spontaneously? Sometimes, some time after I've backgrounded a process with bg in bash, when I press Enter in the same shell to redisplay the prompt (just to check that I'm still in bash when some output from the background process has been displayed), the background process seems to stop spontaneously.  If I do bg again the same problem recurs.  The only way to fix it seems to be fg.  Why does this happen?