Show that $\lim_{n\to\infty} a^{\frac1n}=1$
Proving $\lim_{n\to\infty} a^{\frac{1}{n}}=1$ by definition of limit
Limit of $s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx$ as $n \to \infty$ Let $s_n$ be a sequence defined as given below for $n \geq 1$. Then find out $\lim\limits_{n \to \infty} s_n$.   \begin{align}   s_n = \int\limits_0^1 \frac{nx^{n-1}}{1+x} dx  \end{align}  I have written a solution of my own, but I would like to know it is completely correct, and also I would like if people post more alternative solutions. Why don't researchers request payment for refereeing? Can Europeans reset their "time in Canada" clock by visiting the US? If a Swiss citizen comes to Canada and stays for 6 months, can they travel to USA for example, for a short period of time, and then return to Canada for another 6 months?  How long must they stay out of Canada before returning? How can I pass arguments to a batch file? I need to pass an ID and a password to a batch file at the time of running rather than hardcoding them into the file.  Here's what the command line looks like:  test.cmd admin P@55w0rd &gt; test-log.txt I came across this strange code snippet which compiles fine:  class Car {     public:     int speed; };  int main() {     int Car::*pSpeed = &amp;Car::speed;     return 0; }   Why does C++ have this pointer to a non-static data member of a class? What is the use of this strange pointer in real code? How do I figure out the right size font / text for a given read distance? To avoid printing single letters at varying sizes and measuring how far away I can see it from a distance is there a formula for determining what size font for a particular read distance? Is it better to take the midpoint between the ascender line and x-height or to go purely off of the x-height (since going purely off the ascender line could leave lowercase letters difficult to read)? How does vertical height play into this? Would I need to then figure the hypotenuse distance instead of a straight distance?  For example if I'm shooting for a 20' read distance but the sign is to be placed about 30' up should I use a distance of  35' instead of 20'?  I'm shooting for a 20' read distance for the headline and then possibly a 10' read distance for additional content depending on how it all fits on the active area. My reputation rating on SO took this hit an hour ago, and it is due to what appears to be the simultaneous deletion of multiple questions.  I am uncertain why it happened, am concerned, and would appreciate an explanation.  Going to  shows that it was removed due to moderation.  Was a script run deliberately, or were we hit with a question deletion attack; what happened?  -12     today -2  1 hour ago  removed     How to send a 2d Vector over UDP in c++ -2  1 hour ago  removed     How do I use the Eclipse debugger to debug a Java application? -2  1 hour ago  removed     PHP string error; inconsistency with local and server -2  1 hour ago  removed     Unable to start the MySQL service after a server migration -2  1 hour ago  removed     How to use Java to print a text file on a ticket printer? -2  1 hour ago  removed     How can all of the ZBrush Obj files be imported to make a complete model? Is it possible to bring built-in lightning components into aura component? I have a form that needs to let the user select 3 out of 5 products, something similar to Order > Add Product (Modal). I was wondering if there was a way to bring that piece into my component (markup) and add some sort of filter that only shows the products I want to show.  What I found so far:  &lt;lightning:listView objectApiName="Products2" listName="productsView" showActionBar="true" enableInlineEdit="true" showRowLevelActions="true"/&gt;   But Product2 is not supported for that component.  also these from browser inspector:  forceMultiAddUsingLVM forceListViewManager   These are data-aura-class attributes when rendered.  I'm looking for directions here. Thanks in advance. I have a time series that shows a nonstationary seasonal autoregressive component as well as known heteroshedasticity. In order to model the series, I have fit a seasonal ARIMA model for the mean with the auto.arima model in the forecast package in R and a GARCH model on the residuals of the ARIMA model.   Is the procedure of sequentially estimating ARIMA and GARCH model correct or would it have been better to jointly model the mean and the variance of the series? If this were correct, is there a (possibly R) function to do it? How to prevent nginx redirecting from HTTPS to HTTP on AWS? I have a website served by nginx behind an AWS ELB Load Balancer. Only HTTPS is enabled on the load balancer.  Requesting individual files, or directories with a trailing slash, work fine. However, requesting directories without a trailing slash don't work.  The reason is, when I request the directory without the trailing slash, nginx does a redirect to the path with the trailing slash (that's OK), but it also changes from HTTPS to HTTP. The load balancer is configured to only allow HTTPS, so that doesn't work (timeout).  On the nginx logfile, I can see that the request reaches nginx, and that it's nginx that responds with the 301 Permanent Redirect (so it's not e.g. a problem with the load balancer setup).  10.100.10.15 - - [24/Nov/2017:15:41:08 +0000] "GET /admin HTTP/1.1" 301 178 "-" "Wget/1.18 (darwin16.0.0)"   When I request the URL via curl I see the redirect:  $ curl -v https://example.com/admin *   Trying 1.2.3.4... * TCP_NODELAY set * Connected to example.com (1.2.3.4) port 443 (#0) * TLS 1.2 connection using TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256 * Server certificate: example.com * Server certificate: Amazon * Server certificate: Amazon Root CA 1 * Server certificate: Starfield Services Root Certificate Authority - G2 &gt; GET /admin HTTP/1.1 &gt; Host: example.com &gt; User-Agent: curl/7.54.0 &gt; Accept: */* &gt;  &lt; HTTP/1.1 301 Moved Permanently &lt; Date: Mon, 27 Nov 2017 09:19:05 GMT &lt; Content-Type: text/html &lt; Content-Length: 178 &lt; Connection: keep-alive &lt; Server: nginx &lt; Location: http://example.com/admin/ &lt; X-UA-Compatible: IE=Edge &lt;  &lt;html&gt; &lt;head&gt;&lt;title&gt;301 Moved Permanently&lt;/title&gt;&lt;/head&gt; &lt;body bgcolor="white"&gt; &lt;center&gt;&lt;h1&gt;301 Moved Permanently&lt;/h1&gt;&lt;/center&gt; &lt;hr&gt;&lt;center&gt;nginx&lt;/center&gt; &lt;/body&gt; &lt;/html&gt; * Connection #0 to host example.com left intact   My nginx config file is just   server {     root /var/www; }   The /etc/nginx/nginx.conf is .  I have tried server_name_in_redirect off but it did not make any difference.  I would like to avoid putting the hostname in the config file, because this is packed into a Docker image which is then deployed on different hosts (QA, Prod, etc.).  I would like nginx to do this redirect, but stay on HTTPS. What can I do? I have the following prompt in bash which shows the current git branch:  PS1+="$(git_prompt)" #git_prompt is a function in my .bashrc   which works when I source the .bashrc, but not when I change the branch, so the PS1 var gets only evaluated when I source the .bashrc, but it should be evaluated every time a new prompt is displayed. How can this be accomplished with bash 4.3 ? How to create a fancy table of contents for Beamer How can I create a fancy-looking table of contents for a Beamer presentation?    \documentclass{beamer} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc}  \begin{document}  \frame{ \tableofcontents }  \section{Foo bar} \frame{} \section{Foo bar} \frame{} \section{Foo bar} \frame{} \section{Foo bar} \frame{} \section{Foo bar} \frame{} \section{Foo bar} \frame{} \section{Foo bar} \frame{}  \end{document} If $a_k\geq0$ is a decreasing sequence converging to $0$, do we have $\lim_{n\to\infty}\frac{\sum_{k=1}^n a_k}n = 0$? PHP conditionals, brackets needed? I was just browsing a forum and someone asked about a PHP file they had found on the web.  It has several spots like this in the code:  if ($REMOTE_ADDR == "") $ip = "no ip"; else $ip = getHostByAddr($REMOTE_ADDR);  I have always thought brackets are needed to enclose what you want to do if the condition is true.  Is there some other alternative, such as if it is on the same line you don't?  There is also another line like this: if ($action != ""): mail("$adminaddress","Visitor Comment from YOUR SITE",  My instinct is to say this wouldn't work, but I also don't know if it is an outdated PHP file and it used to work? How can you draw more detailed/smoother images in pygame? This picture is a part of a table i am using, the terms subcases are vertically written but i cant center them vertically also in the next columns terms like A, B, etc are also not vertically centered. I made this table using tabulary package a. My code is  \begin{table}[H]  \centering  \caption{Saturation Table}  \label{tab:5}%  \begin{tabulary}{1\linewidth}{J J J J J J J J J J J J J}  \toprule  &amp; \textbf{Method} &amp; \multicolumn{1}{c}{\textbf{Parameters}} &amp; \textbf{Step 0} &amp; \textbf{Step 1} &amp; \textbf{Step 2} &amp; \textbf{Step 3} &amp; \textbf{Step 4} &amp; \textbf{Step 5} &amp; \textbf{Step 6} &amp; \textbf{Step 7} &amp; \textbf{Step 8} &amp; \textbf{Step 9} \\  \midrule  \multirow{4}[4]{*}{\begin{sideways}\textbf{Subcase A}\end{sideways}} &amp;  \multirow{2}[2]{*}{\textbf{A}} &amp; \textbf{No} &amp; 1 &amp; 2 &amp; 3 &amp; 4 &amp; 5 &amp; \textbf{6} &amp; &amp; &amp; &amp; \\[1mm]  &amp; &amp; \textbf{Maximum Saturation {(\%)}} &amp; 1 &amp; 2 &amp; 3 &amp; 4 &amp; 4 &amp; \textbf{5} &amp; &amp; &amp; &amp; \\  \cmidrule{2-13} &amp; \multirow{2}[2]{*}{\textbf{B}} &amp; \textbf{No} &amp; 1 &amp; 2 &amp; 3 &amp; 4 &amp; 5 &amp; 6 &amp; 7 &amp; \textbf{8} &amp; &amp; \\[1mm]  &amp; &amp; \textbf{Maximum Saturation {(\%)}} &amp; 6 &amp; 6 &amp; 7 &amp; 8 &amp; 9 &amp; 9 &amp; 19 &amp; \textbf{8} &amp; &amp; \\  \bottomrule  \end{tabulary}%  \end{table}% Path.Combine for URLs? is handy, but is there a similar function in the .NET framework for ?  I'm looking for syntax like this:  Url.Combine("http://MyUrl.com/", "/Images/Image.jpg")   which would return:  "http://MyUrl.com/Images/Image.jpg" raw data stationary but still can see trend and seaonality is stl How do you get assembler output from C/C++ source in gcc? How does one do this?  If I want to analyze how something is getting compiled, how would I get the emitted assembly code? Does "it is entirely possible that" require the subjunctive form of the verb following "that"?