Evaluate if the following series is convergent or divergent: $\sum\limits_{n=2}^\infty \frac {1} {n\ln(n)\ln\ln{n}}$.   I cannot properly understand the notation that the book employs here $\ln\ln(x)$, but I guess it is referring to $\ln(\ln(x))$. Assuming $\ln \ln(x)=\ln(\ln(x))$,  I used the Weierstrass's or comparasion test to evaluate the series:  $$\sum\limits_{n=2}^\infty \frac {1} {n\ln(n)\ln\ln{n}}&lt;\sum\limits_{n=2}^\infty \frac {1} {n\ln(n)\ln(n)}=\sum\limits_{n=2}^\infty \frac {1} {n\ln^2{n}}&lt;\sum_\limits{n=2}^{\infty}\frac{1}{n^2},$$ proving the series converge. However the solution point out the series diverge.   I have already proved the convergence $\sum_\limits{n=2}^{\infty}\frac{1}{n^2}$.  Question:  What am I doing wrong? How can I prove the series diverge? Is $\ln\ln(x)=\ln(\ln(x))$ meant by the author of the book?
I'm being asked to determine if $\displaystyle\sum\limits_{n=3}^\infty \frac1{n (\ln n)\ln(\ln n)}$ converges. So, using Cauchy's Condensation Test, I reduced the problem to one of determining the convergence of $\displaystyle\sum\limits_{n=3}^\infty\frac 1{n\ln (n\ln 2)}$. Am I on the right path, and how do I proceed from here?
I'm not quite sure how this happened, but somehow a completely empty hierarchy of directories has ended up in my repository:  com/ com/companyname/ com/companyname/blah/ com/sun/ com/sun/java/ com/sun/java/jax_rpc_ri/   I think what happened was that these directories did have files in them, but then a developer realized he/she shouldn't have checked them in in the first place since these are by-products of the build process, so he/she removed the files but somehow the empty directories are left in the repository as ancient relics.  How can I remove this from CVS? The only results I seem to be able to find on google say that there shouldn't be a need to remove empty directories as CVS won't keep them around in the first place, and that the -P (prune) options to cvs update should remove them from the working directory  - which is zero help if you actually have empty directories in your repository.  A cvs remove and cvs commit doesn't seem to take care of this situation:  $ cvs remove -Rf com cvs remove: Removing com cvs remove: Removing com/companyname cvs remove: Removing com/companyname/blah cvs remove: Removing com/sun cvs remove: Removing com/sun/java cvs remove: Removing com/sun/java/jax_rpc_ri $ cvs commit com cvs commit: Examining com cvs commit: Examining com/companyname cvs commit: Examining com/companyname/blah cvs commit: Examining com/sun cvs commit: Examining com/sun/java cvs commit: Examining com/sun/java/jax_rpc_ri $ ls -l com total 24 drwxrwxr-x  2 matt matt 4096 Oct 15 14:38 CVS drwxrwxr-x  9 matt matt 4096 Oct 15 14:38 companyname drwxrwxr-x  4 matt matt 4096 Oct 15 14:38 sun   It's still there!  Does SVN have this weird behavior too? What screenshot tools are available? I have noticed that many people use images in their Ask Ubuntu answers. What software are people using? I have 2 ADS1299 analog to digital converters(). I need to give them bipolar mode supplying but I must use a powerbank of 5V 3A. I wonder how can I create a bipolar supply of +2.5v -2.5v as mention in the datasheet from the 5V of the powerbank. I am new in this field. Thank you Do I need to apply for a visa to enter South Korea as a tourist on an Australian passport? Do I need to apply for a visa to enter South Korea as a tourist for a few days when travelling on an Australian passport? Or will I be able to get one on arrival? I need to make Windows 7 STOP disabling the wifi adapter when the wired LAN is connected This is a Dell Latitude E6430. There is a setting in the bios to control this behavior and I have DISABLED it but it still happens. I am also running the latest bios.  When I plug in a network cable the wifi adapter becomes disabled. I need it to stay enabled. What else could be making this happen?  EDIT: The reason I need to do this is because with NETSH WLAN commands you can create a wifi hotspot by sharing the internet connection on the wired adapter and broadcasting a ssid on the virtual wifi nic. I do this all the time but it's not working on this laptop. I'm wondering if it's a network security thing where I am. I'm going to try from my hotel tonight and report back. Show that any prime ideal from such a ring is maximal. Do accepted answers still serve a useful purpose? In the Stack Exchange voting system, we have two classes of votes: standard up / down votes that anyone can cast, and special  that only the asker can.   Although accepting an answer does not always pin it at the top of the answer list, that green check mark does  about the correctness of the answer. This gives a single person much greater weight than the rest of the community. That green check mark can seem confusing to visitors, who see  or  answers marked as being correct. I've heard this from several friends recently who were surprised when they came across factually wrong answers that had been downvoted, yet still had that check mark next to them.  Moderators regularly field flags from even more experienced users who demand that the accepted answer be changed from one that is incorrect or even harmful to another. We decline these, because we're not supposed to be making technical judgments like that and because we have no way of accepting answers on behalf of the asker. However, these flags do show that some people have problems with the presentation of accepted answers vs. the community voting on all the others.  There's also all the fun that came with arguments over accept rate, and people badgering askers to accept their answers.   Questions on the Stack Exchange network are intended to be broadly useful, to help out many others in the future beyond the person asking the question. If that's our goal, why should the person asking the question have any more say than the rest of the world? If it's a broadly applicable question, why should one person be able to highlight something as correct simply because they asked it first?  I guess what I'm asking is: if we did away with accepted answers, converting them to upvotes where appropriate, and only let community voting sort out the best answers, would we lose something important? I thought I'd ask after reading  to , because I wasn't sure how I felt about accepted answers anymore. Isn't every subset of a compact space compact? Let $\mathfrak{C}$ be an open cover of a topological compact space $X$, and let $\mathfrak{B}\subseteq \mathfrak{C}$ be its finite subcover. Then every subset of $X$ also has the same cover and subcover! Shouldn't every such subset also be compact then?  Motivation: I read somewhere that every closed subset of a compact space is compact. I wonder why it shouldn't be the case for every subset of $X$, rather than just the closed ones. Do new wire runs in an existing ceiling need to be stapled down? I've heard some people say that code requires wiring in the wall to be stapled to framing every so often (how often?), but when you are doing a remodel, is that necessary?  I have a two story house, and would like to remove one standard dome light on the first floor ceiling and replace it with 6 recessed lights.  There is about 12" of empty space between the floors, and it seems easy enough to run the wire from light to light without cutting any drywall except for the 4-5" holes required for the lights. However, there's no way I'd be able to staple the wiring down.  It's just going to be loose in the ceiling, running through a small hole in the I joists every once in a while.  They sell "remodel" light cans that are made specifically so you only have to cut a hole big enough for them to fit in, so this seems like a common job.  What am I missing and how can I do this job in the most correct way?  This is in Dallas, TX, single family residence. Edited vs emitted - why one t vs two t's Why does "edited" have one "t" and  and "emitted" has two? "Edit" and "emit" are so similar in spelling and pronunciation.  I keep wanting to type "editted" for some reason. I've seen them maneuver. They definitely can go backwards. How fast can they go in reverse? Is warp speed possible, or is reverse limited to impulse power? If it is limited to impulse power, can they travel backwards under impulse power as fast as they travel forwards under impulse power? If $p$ is congruent to $2 \pmod 3$, how can I prove that all $a$, $1 \le a \le p-1$ are cubic residues $\mod p$? If $p$ is congruent to $2 \pmod 3$, how can I prove that all $a$, $1 \le a \le p-1$ are cubic residues $\mod p$?  Here's what I've done:  $1^3$ congruent to $1 \pmod p$ thus, 1 is a cubic residue, Also $(p-1)^3=(p-1) \pmod p$ implies  $$(p-1)^3 - (p-1) = (p-1)[(p-1)^2 -1] = (p-1)(p^2 -2p) = p(p-1)(p-2) $$ implies $$p|(p-1)^3 -(p-1)$$ Thus  $p-1$ is a cubic residue $\mod p$. Now I don't know how to show for $1\lt a \lt p-1$ are all cubic residues when $p$ is congruent to $2\pmod 3$. Why won't my taskbar display on my secondary monitor? On my secondary monitor (currently using Windows 10), my taskbar will barely show up. I've tried adjusting the resolution to lower ones (it recommends 1920x1080) and it doesn't do much. Is there a way to adjust the taskbar so I can see it?  That is about what I see. I could make it bigger via Snipping Tool and see my entire desktop on the picture but not normally. Proof that any self-complementary graph has to have $4k$ or $4k+1$ vertex, for some $k \in \mathbb N$ The subscript size for formulas in beamer presentation First of all sorry because this question may be duplicated. I don't know why the question was uploaded with another user's name and I can't edit it (may be you can delete the previous question with the same title). The question is the following:  I am creating a beamer presentation where I have a lot of formulas. Between the packages used I have \usepackage{amsmath} and the theme for the presentation is \usetheme{Warsaw}.  As it can be seen in the attached picture, the size of the sub(super)script is bigger than the normal writting.     Anyone knows a set of basic packages in order to get the classical formulas, without these size changes?  The code is the following  \documentclass[]{beamer}  \setbeamercovered{transparent}   %--------------------------% % To add enumeration index %--------------------------% \addtobeamertemplate{navigation symbols}{}{%     \usebeamerfont{footline}%     \usebeamercolor[fg]{footline}%     \hspace{1em}%     \insertframenumber / \inserttotalframenumber  } \setbeamercolor{footline}{fg=black} \setbeamerfont{footline}{series=\bfseries}   %---------------------------------------------------------------------------------%  \usepackage{amsmath,amssymb}    % Theme for the presentation \usetheme{Warsaw} % Change the colour \usecolortheme{spruce}  \setbeamertemplate{footline}{}  % Delete the footline with the names    \begin{document}    \begin{frame} \frametitle{\textbf{Algorithm}: step \texttt{s}}   \scriptsize  \textbf{STEP \texttt{s}}  \vspace{0.25cm}  Let $B^{(s-1)}$ be the variable  for the $\mathit{(s-1)}$-th step, let's take the sets $I_+^{(s-1)}$ and $I_-^{(s-1)}$ of length $r_+^{(s-1)}$ and $r_-^{(s-1)}$ respectively,and define:\\  \vspace{0.25cm}  \begin{center}  $B^{(s+)}= \sqrt{\tfrac{(r_+^{(s-1)} + 1)*r_-^{(s-1)}}{r_+^{(s-1)} + r_-^{(s-1)} + 1}} $  \end{center}   \end{frame}  \end{document} If I push or hit an object in space will it rotate or move along a straight line? If I push or hit an object in space (vacuum and no gravitation) in direction what is not going trough its centroid, will it rotate or move along in straight line?   I expect that on earth it will depend on what is less difficult for the object (rotation or linear movement). So the object will do some kind of combination of both movements (rotating and also moving along the direction of impulse or force).  But how could an object "decide" what to do in space, where is not resistance? How to shrink Windows 7 boot partition with unmovable files What book describes consuming vials of vampire blood to pseudo-Rage? Currently, for all my commands that require root access, I have to type them out on a command line.  I would like for the GUI to prompt me to key in my password, when sudo is required, instead of having to type out the commands from command line.  Is there any way to enable this? Previously one version of Ubuntu desktop had this feature out of the box.  This version of Ubuntu (that I am now running) I upgraded from a server installation.  I will add, my user account is already added to sudo group. Thus I can run commands such as sudo gedit or sudo apt-get but I'm not able to install software in the Ubuntu Software Center. What off-camera flash solution should I use with an entry-level Nikon?