Suppose we have bounded, monotonically decreasing $\epsilon_i$, such that as $i \rightarrow \infty, \epsilon_i \rightarrow 0$.   How can I show that $\lim_{n \rightarrow \infty} \frac{\sum_{i=1}^\infty \epsilon_i}{n} = 0$? Is this even necessarily true? Tried Kronecker's lemma, as well as comparison tests to no avail. Seems like a pretty fundamental fact to prove.
Let $y_n$ be a sequence such that  $\lim_{n\to \infty} y_n= y$ then prove that     $ \lim \dfrac{y_1+y_2+...+y_n}{n}= y$   My try:  As  $\lim_{n\to \infty} y_n= y$ then given $\epsilon&gt;0$ there exists $N$ such that $\forall n\ge N ;||y_n-y||&lt;\epsilon $.  Now $||\dfrac{y_1+y_2+...+y_n}{n}-y||\le n^{-1}\{||y_1-y||+||y_2-y||+...+||y_n-y||\}$  How to make this limit tend to zero?
Why isn't an upgrade to 20.04 from 18.04 available yet? I want to use do-release-upgrade to upgrade from 18.04 to 20.04, but I can't do that do-release-upgrade Checking for a new Ubuntu release There is no development version of an LTS available.  It seems that  is used, and it still points to 18.04. Do you know when (or how?) can I upgrade to 20.04? Count and use the number of items in advance Do downvotes on Meta truly mean something different? It is often said that voting on Meta means something different than voting on regular sites. Upvotes mean "I agree", and downvotes mean "I disagree".  However, I submit that this is not the case. Downvoting of a question has one effect in particular: censorship.  Once a question reaches -8 votes, it disappears from the front page. It can still be found; it isn't deleted. But all it takes is a net 8 downvotes for a question to be more or less lost without a direct link.  You might say that a net 8 downvotes obviously means that the community doesn't agree or want that. Well... does it? Particularly on polarizing issues, a question can temporarily get -8 votes as different people come online and see it. Maybe certain people with a certain belief all see it at once and downvote it a lot.  The front page is how most people find stuff they want to talk about, vote on, or answer. Removal from the front page means that most people will not find it without being pointed directly to it. Once a question hits -8, it is unlikely to be upvoted again. Edits will be irrelevant, new answers won't matter. The question is basically exiled.  The problem is that, on polarized topics, fast mass downvoting can quash any idea that is not popular with the most active members. After all, the most active members are the ones who are most likely to be online and see it. If a bunch of MSO regulars see it and downvote it, it goes away. Someone who checks MSO maybe once a day is less likely to be able to catch the question before it is exiled. This gives undue power to members who are most active on MSO, simply because they have more free time to spend on MSO.  I think this is a significant problem for polarized topics. It becomes very difficult to adequately discuss something that a significant number of active members dislike, even if the community at large doesn't mind.  Consider . It currently stands at +9/-8. Initially, in the first few hours, the question was heavily downvoted and even closed. However, after a day, it was upvoted and reopened.  This shows that a question can initially have a negative response, but later get a positive one. And you can check; any edits I did to the question were relatively minor. The question posted as is was initially negative, but ultimately positive.   If that -8 happened to all come first, odds are good that the +9 and the reopen would never have happened. Those 9 people would never have had the chance to weigh in on the subject. And that's wrong.  It is wrong for someone's potential vote to not matter just because they don't visit MSO multiple times in a day. It is wrong for someone's potential vote to not matter just because they have a different sleep schedule from many of MSO's members.  The problem is one of timing. Heavy dislike from active members who quickly see the question and downvote it can kill a question before someone who might upvote it ever even sees it.  I suppose the best suggestion would be to either lower the -8 threshold (or remove it altogether) or keep it from kicking in until 1-2 days has passed. If the question isn't active, it'll already be off the front page. And if it is active, then enough people will have seen it to know if the threshold represents a real consensus or just the fast-acting few. How can i integrate one SFDC org to another SFDC using Rest Api I am trying to integrate one Salesforce org to other org by using Oauth setup, I wanted to use  use consumer key and consumer secret key in my REST class to connect with the org, after connection part completion, I want to access Get(), Put(), Post(), etc. Including the ability to set Oauth and Authorization headers needed for Salesforce Rest API calls.  Actually I'm new in REST implementation so can you please explain me by using code samples. I have Lubuntu 16.10 installed on my disk mounted as /.  The problem is that the CUPS log file( /var/log/cups/error.log)  grows all the time until I no have free space left on the disk...   So when I delete that file, the space on disk freed up again  I already tried:    fsck disk usage analyzer every apt-cleaning/autocleaning, and dependencies fixing.    How should I proceed?  du -sxh:  9,0G    .  Model: ATA ST3160815AS (scsi) Disk /dev/sda: 160GB Sector size (logical/physical): 512B/512B Partition Table: msdos Disk Flags:   Number  Start   End     Size    Type      File system     Flags  1      32,3kB  50,3GB  50,3GB  primary   ext4            boot  2      50,3GB  160GB   110GB   extended  5      50,3GB  158GB   108GB   logical   ext4  6      158GB   160GB   2136MB  logical   linux-swap(v1)   parted --list &amp;&amp; sudo df -h:  Model: ATA ST3160815AS (scsi) Disk /dev/sda: 160GB Sector size (logical/physical): 512B/512B Partition Table: msdos Disk Flags:   Number  Start   End     Size    Type     File system  Flags  1      32,3kB  50,3GB  50,3GB  primary  ext4         boot  2      50,3GB  160GB   110GB   primary  ext4   Filesystem      Size  Used Avail Use% Mounted on udev            985M     0  985M   0% /dev tmpfs           201M  6,3M  195M   4% /run /dev/sda1        46G   43G  709M  99% / tmpfs          1003M  188K 1003M   1% /dev/shm tmpfs           5,0M  4,0K  5,0M   1% /run/lock tmpfs          1003M     0 1003M   0% /sys/fs/cgroup tmpfs           201M   36K  201M   1% /run/user/1000 /dev/sda2       101G   60M   96G   1% /media/aram/ Broadcom Wireless Drivers unclaimed after installing update 16.04 The mysql extension is deprecated and will be removed in the future: use mysqli or PDO instead Having changed the scene units and unit scale, how can I change the default size of new objects? I am using blender most of the time to model things for my 3d printer. So a default unit in "meters" is not really helpful!  Within the scene settings it is simply possible to set the units to millimeter and the unit scael to 0.001 so everything seems to work as I want it to work...   But if I add a new primitive it uses its old default sizes in meters... so a new cube get's 2000 x 2000 millimeters instead of 2x2 or whatever will be useful..  Same for all other new objects...  How can I change the default sizes of new objects permanently?   And how can I change the settings in the application templates? Right now using ctrl+u changes the "general" template - perhaps because I loaded it before...   Thanks a lot and best regards Stefan I want to hit enemy's axe to break it. How this is properly played in D&amp;D 5e? And what about shield or armor? Can I attack these items to break it? Feedback for The Loop - May 2020 May’s “The Loop” blog post was just posted, you can read it . A popular response last month to our post about how we receive, prioritize and implement feedback was a question around how this framework gets utilized in the practical sense. We thought that Dark Mode was a great feature to dig down into as it was so widely requested and anticipated.   We hope you enjoy this month’s post, please leave any questions or comments you have in this thread and we will respond ASAP. How do you make an image emission without washing out the image? I am trying to make a computer monitor. This means I have to have an image texture for the screen. My image texture is currently connected to an Emission BSDF shader. Unfortunately, when the emission is bright enough to emit light, the image is white-washed. I tried adding a Brightness/contrast node to the image before pushing it into the Emission BSDF, but it seems to directly counter the Emission's strength.  The desired light level   The desired image brightness Drawing a 3D cylinder, and a circle shape on the x---y plane I'm trying to draw a cylinder on the three dimensional space, and I also want its projection on the x--y plane. I found the first answer  to be very useful. I just copy-paste it to my document, and modify it as follows (the modifications are only inside the \begin{tikzpicture} tags):   \documentclass[parskip]{scrartcl} \usepackage[margin=15mm]{geometry} \usepackage{tikz}  \pgfmathsetmacro{\xdeg}{30} \pgfmathsetmacro{\xx}{cos(\xdeg)} \pgfmathsetmacro{\xy}{sin(\xdeg)}  \pgfmathsetmacro{\ydeg}{120} \pgfmathsetmacro{\yx}{cos(\ydeg)} \pgfmathsetmacro{\yy}{sin(\ydeg)}  \pgfmathsetmacro{\zdeg}{80} \pgfmathsetmacro{\zx}{cos(\zdeg)} \pgfmathsetmacro{\zy}{sin(\zdeg)}  \newcommand{\tdcyl}[5]{% origin x, origin y, origin z, radius, height     \path (1,0,0);     \pgfgetlastxy{\cylxx}{\cylxy}     \path (0,1,0);     \pgfgetlastxy{\cylyx}{\cylyy}     \path (0,0,1);     \pgfgetlastxy{\cylzx}{\cylzy}     \pgfmathsetmacro{\cylt}{(\cylzy * \cylyx - \cylzx * \cylyy)/ (\cylzy * \cylxx - \cylzx * \cylxy)}     \pgfmathsetmacro{\ang}{atan(\cylt)}     \pgfmathsetmacro{\ct}{1/sqrt(1 + (\cylt)^2)}     \pgfmathsetmacro{\st}{\cylt * \ct}     \filldraw[fill=white] (#4*\ct+#1,#4*\st+#2,#3) -- ++(0,0,#5) arc[start angle=\ang,delta angle=-180,radius=#4] -- ++(0,0,-#5) arc[start angle=\ang+180,delta angle=180,radius=#4];     \filldraw[fill=white] (#1,#2,#3+#5) circle[radius=#4]; }       \begin{tikzpicture}[x={(\xx*1cm,\xy*1cm)},y={(\yx*1cm,\yy*1cm)},z={(\zx*1cm,\zy*1cm)}]          \tdcyl{-3}{-3}{0}{1}{3} % x y z   r h         \tdcyl{0}{0}{0}{1}{3} % x y z   r h           \draw (-3,0,0) -- (3,0,0) node[circle,fill=white] {x};         \draw (0,-3,0) -- (0,3,0) node[circle] {y};         \draw (0,0,-3) -- (0,0,3) node[circle] {z};     \end{tikzpicture}     \end{document}   I added another cylinder and tweaked the positions to fit what I need. This produces the following:      Which is almost what I want, except that I want to see the projection of that cylinder on the x--y plane, but unfortunately, the top cylinder hides the full circle. When I disable the top cylinder:      \begin{tikzpicture}[x={(\xx*1cm,\xy*1cm)},y={(\yx*1cm,\yy*1cm)},z={(\zx*1cm,\zy*1cm)}]          \tdcyl{-3}{-3}{0}{1}{3} % x y z   r h            \draw (-3,0,0) -- (3,0,0) node[circle,fill=white] {x};         \draw (0,-3,0) -- (0,3,0) node[circle] {y};         \draw (0,0,-3) -- (0,0,3) node[circle] {z};     \end{tikzpicture}   Now the projection is shown again:   But the top cylinder is missing...  How can I make the top cylinder transparent, or, alternatively, and even better; how do I create one long cylinder and emphasize its projection on the x--y plane?   BTW, what determines the position of the labels x,y,z in the above code? I want to reposition them so they won't overlap with the axis. Thanks in advanced! I am new to working with IDS' such as Suricata/Snort. I am currently trying to using Suricata to log DNS requests and responses to malicious domains on my network. On my DNS server I made it so that any request to say, bad.com, would resolve to 127.0.0.1, thus not allowing anybody on my network to access that site.   I have set up Suricata to log all DNS requests, but how do I filter that down and narrow it and tell it to only log requests to 127.0.0.1 and let everything else go unlogged?   I tried to create a rule:  alert dns any any -&gt; 127.0.0.1 any (msg: "BLACKLISTED WEBSITE"; flow:to_client; content:"rrname";sid:2240001;rev:1;)   But that did not work.   What do I need to do to only log DNS requests to certain IPs? I cannot find any information in the documentation or anywhere else on the internet.   Thanks. Why (...) doesn't spawn a new child process when run in background? Can't do reviews after failing 1 audit I'm at a loss with “Dungeons and Dragons.” How does one play it, anyway? I'm no gamer at all, so this could be like a very silly, basic question for you guys. The thing is that I always read about "Dungeons and Dragons" game (not the video game, but the normal game to play with friends that are actually gathered together). And I would like to know how to play it.  I've read that it is a book (or several ones, which is more confusing for me to understand), but I've read somewhere that it can be played as a normal "table" game, with a board, and pieces, and somewhat weird dice (or sets of dice).  Is it like a normal game, where you pull the stuff out of a box and start to play?  I don't know if any of you watch the show "The Big Bang Theory", but I think they have played the game in a recent episode, and it looks just like a regular game.  I've Googled it for more information, but I haven't found anything as basic as I need, because I've never played a role game (except in a video game).  I just want to learn how to play, so I can get my friends into it to play it each time we get together. This is a follow-up to .     When I click a link to an SE site in the Android app, it gives me an "open with" pop-up that has two options:         Chrome   Stack Exchange         I can then choose to open SE posts like this "Just once" or "Always."      The problem is that when I set the SE app to "always," and I click "open in browser,"   Except, the app crashes when trying to open it in browser.  LogCat (just right after selecting "Open in browser")  01-22 18:03:36.354: E/AndroidRuntime(16064): FATAL EXCEPTION: main 01-22 18:03:36.354: E/AndroidRuntime(16064): Process: com.stackexchange.marvin, PID: 16064 01-22 18:03:36.354: E/AndroidRuntime(16064): java.lang.NullPointerException: Attempt to invoke interface method 'int java.util.List.size()' on a null object reference 01-22 18:03:36.354: E/AndroidRuntime(16064):    at com.stackexchange.marvin.utils.Helpers.getNonMarvinViewIntent(Helpers.java:452) 01-22 18:03:36.354: E/AndroidRuntime(16064):    at com.stackexchange.marvin.ui.question.QuestionDialog$1.onClick(QuestionDialog.java:39) 01-22 18:03:36.354: E/AndroidRuntime(16064):    at com.android.internal.app.AlertController$AlertParams$3.onItemClick(AlertController.java:1108) 01-22 18:03:36.354: E/AndroidRuntime(16064):    at android.widget.AdapterView.performItemClick(AdapterView.java:310) 01-22 18:03:36.354: E/AndroidRuntime(16064):    at android.widget.AbsListView.performItemClick(AbsListView.java:1145) 01-22 18:03:36.354: E/AndroidRuntime(16064):    at android.widget.AbsListView$PerformClick.run(AbsListView.java:3066) 01-22 18:03:36.354: E/AndroidRuntime(16064):    at android.widget.AbsListView$3.run(AbsListView.java:3903) 01-22 18:03:36.354: E/AndroidRuntime(16064):    at android.os.Handler.handleCallback(Handler.java:739) 01-22 18:03:36.354: E/AndroidRuntime(16064):    at android.os.Handler.dispatchMessage(Handler.java:95) 01-22 18:03:36.354: E/AndroidRuntime(16064):    at android.os.Looper.loop(Looper.java:148) 01-22 18:03:36.354: E/AndroidRuntime(16064):    at android.app.ActivityThread.main(ActivityThread.java:5417) 01-22 18:03:36.354: E/AndroidRuntime(16064):    at java.lang.reflect.Method.invoke(Native Method) 01-22 18:03:36.354: E/AndroidRuntime(16064):    at com.android.internal.os.ZygoteInit$MethodAndArgsCaller.run(ZygoteInit.java:726) 01-22 18:03:36.354: E/AndroidRuntime(16064):    at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:616)   I suspect it's related to , but not sure.  Specs:   Device model: Nexus 5 Android version: Android 6.0.1 SE app version: 1.0.82 (beta) Installed browser: Chrome 47.0.2526.83 (latest at current writing) How does $ \sum_{p<x} p^{-s} $ grow asymptotically for $ \text{Re}(s) < 1 $? A problem with my reasoning in a problem about combinations Which of the following is most correct?      The distance of the shortest path must not be higher than 10km.   The distance of the shortest path must not be greater than 10km.   The distance of the shortest path must not be bigger than 10km.   Or is there an even better word?