$\sum_{n=0}^{\infty}a_n$ diverges in the regular term but is Cesaro summable     Prove $a_n/n\to 0$ when $n\to \infty$   We used the definition of the Cesaro sum and obtained:  $\lim_{N\to \infty}\frac{1}{N+1}\sum_{n=0}^{N}S_n$=$\lim_{N\to \infty}\frac{1}{N+1}\left (  \sum_{n=0}^{N-1}S_n+\sum_{k=0}^{N}a_k\right )$=$\sum_{n=0}^{N-1}\frac{S_n}{N+1}$$+\sum_{k=0}^{N}\frac{a_k}{N+1}$=$L$  but from here we're kind of stuck  *($S_n$ is the partial sums of $a_n$)
Theorem.  If $\sum_{n=1}^{\infty}c_{n}$ is Cesaro summable, then $c_{n}/n$ tends to $0$.  How to prove it?
Why are my SVG imports so small? I'm definitely a newbie with blender still, as I've dipped my toe in a bit being a video editor.  My issue is importing .svg saved from illustrator.  Just simple vectors with not too many paths.  Just a thick text company logo.  I want to bring in and extrude, light, etc.  I've done it before in older versions of blender with no problem.  Am I not doing something right? Can someone tell me how to get an eps saved as an svg from illustrator to size correctly? What is the easiest way to handle huge numbers in C? I need to store values in the Area 1000^900, or in more human readable form 10^2700. Does anybody know of an easy way to do that? Any help would really be appreciated! I've installed Ubuntu 16.04 on my Asus X555LJ.  But I don't know how to install drivers or how to enable function keys to controls screen backlight brightness. Running JAR file on Windows I have a JAR file named helloworld.jar. In order to run it, I'm executing the following command in a command-line window:  java -jar helloworld.jar   This works fine, but how do I execute it with double-click instead? Do I need to install any software? How to run scripts without typing the full path? If $A\subset\mathbb{R^2}$ is countable, is $\mathbb{R^2}\setminus A$ path connected? Possible Duplicate:          As the topic,if $A\subset\mathbb{R^2}$ is countable, does $\mathbb{R^2}\setminus A$ path connected??? I know the answer is it is path connected but not sure how to prove it. I know  that uses $x={\sqrt{2}}^{\sqrt{2}}$ to prove that there must exist an irrational to an irrational power that evaluates to a rational. But I don't know if $x$ itself is known to be irrational or rational.  Could someone enlighten me? Thanks! Showing arrowheads in line end using QGIS? How large is it possible for a PC to get? How large is it possible for a PC to get?  For clarity, here are my parameters:   This is about size categories, not 'feet' or 'inches' or 'meters' or any other precise measurement. This is about Medium to Large to Huge to Gargantuan categories.  This is for an NPC charlatan using this to trick people. (It's an NPC but will have a full PC sheet, so the distinction between PC and NPC doesn't matter). Any means of size category enlargement works for this purpose, including magic spells, magic items, etc. Illusions do not count because it's about actually becoming larger, not just casting an illusion of a gargantuan giant version of yourself.  The character must remain the same physical structure. Polymorphing into a Gargantuan Dragon would not satisfy the need here. Consumable items are fine. This does not need to be permanent. Annoying space before the first item in an enumeration which starts a theorem Consider the following example:  \documentclass{article} \newtheorem{Theorem}{Theorem} \begin{document} \begin{Theorem} On the other hand, this one has only one claim. \end{Theorem} \begin{Theorem} \begin{enumerate} \item First claim \item Second claim \end{enumerate} \end{Theorem} \end{document}   Typesetting it results in:    Notice there is extra horizontal space before the first item in the list of the second theorem.     Is there a sensible way to get rid of that?   Ideally, the solution would work with amsthm, thmtools, enumitem.  N.B.: this is related to  but not quite the same. How do I Parameterize a null string with DBNull.Value clearly and quickly I applied for a 90-day visa and got a long-term visit, single-entry tourist visa. The date given is 09-March-2015, and it's valid until 07-May-2015.  My agent says the 7th is the latest date I can travel to Dubai; once I enter I need to count 90 days. I entered on the 10th of March.    Is it true, or where can I get it checked?    Can I stay for another month, or do I need to leave before the 7th of May? Prove that $\binom{m+n}{m}=\sum\limits_{i=0}^m \binom{m}{i}\binom{n}{i}$ What should the standard spelling be - British or US? gpgkeys: key C927EBE00F1B0520 not found on keyserver Possible Duplicate:    I am using 10.04 LTS - Lucid Lynx. I shutdown the computer while a software update was running. Then after I restarted my computer and while the update manager was running, I got this error:  Could not download all repository indexes The repository may no longer be available or could not be contacted because of network problems. If available an older version of the failed index will be used. Otherwise the repository will be ignored. Check your network connection and ensure the repository address in the preferences is correct. GPG error: http://toolbelt.herokuapp.com ./ Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY C927EBE00F1B0520 Failed to fetch  http://ppa.launchpad.net/rabbitvcs/ppa/ubuntu/dists/**DISTRIBUTION**/main/binary-i386/Packages.gz 404  Not Found   I went through the answers to  and I tried this $ sudo launchpad-getkeys  Please wait... launchpad-getkeys is running an update so it can detect the missing GPG keys Trying to import all the missing keys gpg: requesting key 0F1B0520 from hkp server keyserver.ubuntu.com gpgkeys: key C927EBE00F1B0520 not found on keyserver gpg: no valid OpenPGP data found. gpg: Total number processed: 0 launchpad-getkeys has finished importing all missing GPG keys.  Try running sudo apt-get update - you shouldn't see any key  errors anymore  But when I run sudo apt-get update again, it again shows that the key was not found on the keyserver. How to solve this problem? Use of a semicolon before and comma after "however" Several years ago, a previous boss told me to use a semicolon and comma with the word "however".  I've always questioned this and would like to know if the following random sentences are using the correct method.        Our plane was delayed overnight; however, the airlines reimbursed us for lodging.   It looks as though he's upset; however, she told me he always has that look on his face.   I want to find him a nice gift; however, I am a broke until payday.      Normally I would use a less "wordy" sentence in casual writing, but hopefully the example will suffice.  For example, on number 3 I would usually type:      I want to get him a nice gift, but I'm broke until payday. If I took a picture of a windmill on the horizon — given that I know the sensor size and the focal length of the lens and other factors to do with the shot — could I calculate how far away an object is from the photographer? A customer has a 6-screen setup for each workstation and would like various pages of a web app to be opened automatically in each of the screens on startup or invoking a shortcut. (The target web browser is likely to be Chrome).  I wondered whether it would be possible to use Javascript window.open to do this but one possible snag is the customer may wish to have tabbed browsing with popup blocker turned on. (OK, these could be overridden but such config is currently out of our control...)  So the question is: Could a script (e.g. batch file) be written to open multiple instances of the browser at specified coordinates within the 6 screens (each pointing to different URLs)?  [This is basically the same question as  but for Windows instead of Ubuntu.] How can I add certain mobs to a team and make them passive to me if they would normally attack me? I know how to do it in 1.8, but how can I do it now in 1.16.4? How do I iterate over the properties of an anonymous object in C#?