How can I solve this limit: $\lim_{n\to \infty } \left(\frac{1}{1+n} + \frac{1}{2+n} + ... + \frac{1}{2n} \right) $?
The limit of truncated sums of harmonic series, $\lim\limits_{k\to\infty}\sum_{n=k+1}^{2k}{\frac{1}{n}}$
Let's say we have one black hole that formed through the collapse of hydrogen gas and another that formed through the collapse of anti-hydrogen gas. What happens when they collide? Do they (1) coalesce into a single black hole or do they (2) "annihilate" into radiation?  One would expect (1) to be the case if the No Hair Theorem were to hold. So I guess what I'm really asking for is a modern understanding of this theorem and its applicability given what we know today. $F(x)$ versus $F[x]$ where $F$ is a field Can I mask an input text in a bat file? What good CAD programs are available? Prove the map has a fixed point Assume $K$ is a compact metric space with metric $\rho$ and $A$ is a map from $K$ to $K$ such that $\rho (Ax,Ay) &lt; \rho(x,y)$ for $x\neq y$. Prove A have a unique fixed point in $K$.  The uniqueness is easy. My problem is to show that there a exist fixed point. $K$ is compact, so every sequence has convergent subsequence. Construct a sequence ${x_n}$ by $x_{n+1}=Ax_{n}$,$\{x_n\}$ has a convergent subsequence $\{ x_{n_k}\}$, but how to show there is a fixed point using $\rho (Ax,Ay) &lt; \rho(x,y)$? Gameplay programmers write game code, but so do game designers and developers. Where is the line drawn? What skills do gameplay programmers use that game designers or developers do not? If $a+\frac1b=b+\frac1c=c+\frac1a$ for distinct $a$, $b$, $c$, how to find the value of $abc$? If $a, b, c$ be distinct reals such that $$a + \frac1b = b + \frac1c = c + \frac1a$$ how do I find the value of $abc$?  The answer says $1$, but I am not sure how to derive it. Remove rogue app from menu bar Term or phrase describing action occuring when not watching I am an IT professional. More specifically in automation. I am looking for a term or phrase that describes the event when either:  a. you are watching something closely and the issue doesn't occur  or  b. you are not watching something at all and the issue does occur Do Indian passport holders with UK Tier 2 need to get a tourist visa for Mexico? I'm an Indian passport holder currently resident in the UK under a Tier 2 (General) visa and planning on going to Mexico on a holiday. So I was looking into the rules on the Mexican embassy in the UK and :     According to the new regulations who entered into effect on 18th, May   2016 (article 26 of the Guidelines and Requirements for Migratory   Services) regarding foreign nationals visiting Mexico, holders of a   valid UK visa, regardless their nationality, are not required to apply   for a Mexican visa as a tourist, business (Non-Lucrative Activities)   or transit visitors for a stay of up to 6 months. This regulation does   not apply to British Travel Document holders.   However, :     PERMANENT RESIDENT IN THE UK (ILR / ILE / PERMANENT RESIDENTS)        According to Mexican regulations which came into force in June 2009,   Permanent residents in the United Kingdom wishing to travel to Mexico   do not require a visa to enter the country as tourists or business   visitors for up to 180 days and as visitors in transit for up to 30   days, regardless their nationality.   So which one is correct? Are Tier 2 holders with an Indian passport allowed visa-free / visa on-arrival entry to Mexico? When you add an image strip to the Video Sequence Editor, it stretches/shrinks your image to fit the full output frame.  How can I add an image at its original resolution?  For example, if I add a 60x60 pixel image, it should appear very small in the final 1080p render. When to use LinkedList over ArrayList in Java? Is Autopilot Openstack 16.04 available? Why is uniform prior on log(x) equal to 1/x prior on x? I'm trying to understand Jeffreys prior. One application is for 'scale' variables like the standard deviation $\sigma$ (or its square, the variance $\sigma^2$) of Gaussian distributions. It is often said that using a uniform prior over $\sigma$ is not really non-informative and instead one should either:   Use instead $\ln \sigma$ as the free parameter, with a uniform prior (this is often called a log-uniform prior) Or keep using $\sigma$ as the free parameter but use $1/\sigma$ as the prior (which is not uniform).   Why are the above two methods/priors equivalent? I feel it has something to do with the fact that the derivative of ln $\sigma$ is $1/\sigma$ but I can't take the next step.   Also, why does this even matter, in simple language with minimal jargon? I see all these complicated explanations online involving the Fisher information matrix but in the end all I see is that the above log-uniform or $1/\sigma$ priors preferentially weight lower values of $\sigma$ more highly. Why? If possible, a simple analytic example or python snippet would be very helpful. Rebel flight suits include an ejection harness, Biggs tells Porkins to eject. This seems to suggest that Rebel fighters have an ejection system.  How would they operate for different fighters? Does the whole cockpit separate? Do they function like current aircraft ejection systems - if so what protects the pilot from the vacuum of space? I am a new user, who has just been told to run / execute a command. The answer has some text with a grey background like this text here or  sometimes this text here.   However, I don't know what "run" or "command" means in relation to Ubuntu.  How do I do this?    This is intended for use as a Q&amp;A you can link to when you tell someone to run a command. What I am trying to do is to set a date in my date field and also update the object. I am using the class below to do so which works just fine in my sanbox but in production I am getting this error:      System.LimitException: Too many query rows: 50001   public with sharing class updateObject{     public  List&lt;NRProducts__c&gt;  values;     public PageReference updateObject() {         values=[SELECT Refreshed_Date__c FROM NRProducts__c ];         for (NRProducts__c s :values){            s.Refreshed_Date__c =Date.today();          }          update values;         return null;                       }     }   VF Page:  &lt;apex:page showheader="false" controller="updateObject" sidebar="false"&gt; &lt;apex:form&gt;  &lt;apex:commandButton action="{!updateObject}" value="Update"/&gt; &lt;/apex:form&gt; &lt;/apex:page&gt; Galois Group of $\sqrt{2+\sqrt{2}}$ over $\mathbb{Q}$ Is there a BNF grammar of the TeX language? I'm looking for a BNF grammar of the TeX language, does it exist?  EDIT  For those of us who are not computer scientists, a BNF grammar is one kind of formal description of a CFG: .  For those who don't know their Chomsky, a CFG is a , which means (very roughly) that substitutions can be made independently of their use context. What's the difference between Google Chrome and/or Chromium? What are the advantages/disadvantages to each? I used Google Chrome in Windows, and am now using Chromium in Ubuntu.  Is there any difference to the two programs?  What are the advantages and disadvantages to each program?  Which one seems better?