Proving if $\lim_{n\rightarrow\infty}a_n=L $ then $\lim_{n\rightarrow\infty} \frac{a_1+a_2+\cdots+a_n}n=L $
Suppose $\lim \limits_{n \to ∞} a_n=L$. Prove that $\lim\limits_{n \to ∞} \frac{a_1+a_2+\cdots+a_n}{n}=L$
Changing Network Interfaces name Ubuntu 16.04 I tried to change network interfaces name on this new Ubuntu 16.04 LTS version but doesn't have the /etc/udev/rules.d/70-persistent-net.rules.  So, I tried to use /lib/udev/write_net_rules but it not exist.  Why do I need this modification? Because I'm using a tool to Simulate virtual platforms that use flex licensing and the authentication need to be in eth0 interface name.  Any suggestion?  The command ip link returns:  user@laptop:~$ ip link  1: lo: &lt;LOOPBACK,UP,LOWER_UP&gt; mtu 65536 qdisc noqueue state UNKNOWN mode DEFAULT group default qlen 1 link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00 2: enp6s0: &lt;NO-CARRIER,BROADCAST,MULTICAST,UP&gt; mtu 1500 qdisc pfifo_fast state DOWN mode DEFAULT group default qlen 1000 link/ether b8:2a:xx:yy:xx:yy brd ff:ff:ff:ff:ff:ff 3: wlp7s0: &lt;BROADCAST,MULTICAST,UP,LOWER_UP&gt; mtu 1500 qdisc mq state UP mode DORMANT group default qlen 1000 link/ether 5c:e0:xx:yy:xx:yy brd ff:ff:ff:ff:ff:ff  user@laptop:~$ ifconfig  enp6s0    Link encap:Ethernet  HWaddr b8:2a:xx:yy:xx:yy   lo        Link encap:Local Loopback   wlp7s0    Link encap:Ethernet  HWaddr 5c:e0:xx:yy:xx:yy     (Some information were ignored and suppressed)  I already tried some links: Black shadows on Faces, not a normals thing Why didn't the basilisk bite in Chamber of Secrets destroy the Horcrux? What's the difference between an inverter with a bubble at the input and one with a bubble at the output? See , page 2: the internal logic diagram for the MM74HC138.    The diagram shows logic inverters with bubbles at the input or at the output. Is there an actual difference between them? Cardinal of quotient rings of gaussian integers. It is known that $\mathbb{Z}[i]$ is a PID and that $\mathbb{Z}[i]/(a+bi)\mathbb{Z}[i]$ is finite for all $(a,b) \in \mathbb{Z}^2\backslash \{(0,0)\}$.  My question :      Is there any result on the cardinal of  $\mathbb{Z}[i]/(a+bi)\mathbb{Z}[i]$ ? "Awesome" vs. "Awful" If tenured staff are virtually unsackable, why is the drive to find funding so strong? A Linear Diophantine Equation is of the following form:                                                                                        $Ax+By+C=0$, where $x_1 \leq x \leq x_2$ and $y_1 \leq y \leq y_2$.  If the value of $A,B,C,x_1,x_2,y_1,y_2$ are given and $x_1 \leq x_2$ and $y_1 \leq y_2$, then how many solutions can be found? How can I find out the total number of solutions according to the above condition. My computer boots to a black screen, what options do I have to fix it? I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents: How many rationals of the form $\large \frac{2^n+1}{n^2}$ are integers? I'm having issues unlocking my Nexus 7 2013 WiFi's bootloader, and it was suggested that I try fastboot oem unlock-go instead of fastboot oem unlock. Both seem to act the same on my device, however both also fail on my device so it is possible that the difference appears after the failure on my end comes. Regardless, I would like to know: What is the difference between these two commands? I'm not managing to find documentation. How does Meta Stack Exchange work? Meta Stack Exchange seems to have different rules and user behavior than the "regular" Stack Exchange sites.  How is it different?    Individual questions answered below:                Related What happens to global variables declared in a DLL? Let's say I write a DLL in C++, and declare a global object of a class with a non-trivial destructor.  Will the destructor be called when the DLL is unloaded? 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 was answering a question on Stack Overflow and required to use a trailing space in one of my code snippets.  I formatted it like so:  `&lt;a `   And it renders without the trailing space: &lt;a  Using the &lt;code&gt; tag does account for trailing spaces, though in my case it busts because of the &lt;. Here's my formatting with the &lt;code&gt; tag:  &lt;code&gt;&lt;a &lt;/code&gt;   Here's how it renders:  (Yes, you should see nothing there).  This is a pretty annoying bug. Can we get it fixed? CSS customized scroll bar in div Missing $ inserted I am working on the following problem from group theory:     If $G$ is a group of order $2n$, show that the number of elements of $G$ of order $2$ is odd.   That is, for some integer $k$, there are $2k+1$ elements $a$ such that $a \in G,\;\; a*a = e$, where $e$ is the identity element of $G$. How to prove ${n \choose p} \equiv\left\lfloor \frac{n}{p} \right\rfloor\pmod p$ Prove ${n \choose p} \equiv \left\lfloor \frac{n}{p} \right\rfloor \pmod p$   ($n$ is natural and $p$ is a prime number)  How can i prove this statement? Find and replace text within a file using commands