Given $a_1 =1, a_{n+1}=a_n+e^{-a_n}$. Prove that $b_n:=a_n-\ln(n)$ converges
sequence $x_{n+1}=x_n+e^{-2018x_n}$
Modular exponentiation by repeated squaring For example:     Is (A &or; B &or; C) &and; (D &or; E &or; F) the same as   (A &and; D) &or; (A &and; E) &or; (A &and; F) &or; (B &and; D) &or; (B &and; E) &or; ( B &and; F) &or; (C &and; D) &or; (C &and; E) &or; (C &and; F)?   How would I check equivalence in general? How many times can an Australian leave and re-enter South Africa (90 days at a time without a visa) in a year, and do they need to be out of the country for a certain period of time before they re-enter?  I want to be in South Africa for as long as I can, however as an Australian without a visa I can only stay for 90 days at a time. What I would like to do is simply leave South Africa and go to another country in Africa for a few days, before returning with a new 90 day allowance.    Is this possible, or must I wait a certain period before re-entering South Africa/is there a limit to the amount of times I can do this in one year? How can I shutdown my Android phone using an adb command? How do I halt an android phone using adb command? I can reboot, but I don't know how to halt.  I tried shutdown -k wait command, but it did not work. I have two passports/nationalities. How do I use them when I travel? Proving Geometric Hahn-Banach Implies Analytic Hahn-Banach I've come across a proof online of the H.B theorem using the goemetric version.   There is a step in the proof which im not sure why is true and it is as follows:   Let $X$ be a linear space and $M \subset X \times \Bbb R$ be a maximal subspace.  Then $M = G(F)$ for $F :X \to \Bbb R$ linear.   Someone can show me why this is true?   Maybe I misunderstood the proof, its the last paragraph of Matrin's answer here -.   Thanks a lot for helping! Not every open set in $\mathbb{R}^n$, for $n\geq2$, is a disjoint union of countable open balls. I know that every open set in $\mathbb{R}$ can be decomposed as the union of countably many disjoint open intervals and I'm trying to show that this property no longer holds in higher dimensions. For this I'm trying to show that there is no countable, pairwise disjoint open balls whose union is the open square $(0, 1)^2 ⊂ \mathbb{R}^2$. I know that it is because of the corners, but I don't know how to write this in mathematical terms. Thanks for any help. Website logo text - best tag for SEO purposes? I'm trying to develop a new website in HTML5 adhering to SEO standards where possible and I'm having a little trouble trying to figure out what tag my site name and slogan should live in.  Originally I had my site name in a &lt;h1&gt; tag and my sloagan in a &lt;h2&gt;, but soon realised this wasn't fitting with the "each page is a separate document/article" approach.  The site name is the largest text on the page (sometimes the same as my article heading), but I've currently got the text in a &lt;p&gt; tag with CSS doing all the styling work.  My questions is, what should I do with the site name and slogan? Is the &lt;h1&gt; appropriate, then use another &lt;h1&gt; tag for each page title or should I continue using the styled &lt;p&gt; tag? Or should I convert this into an image and use that for the site name/slogan?  (Side note: on my index page I want the site name and slogan to be &lt;h1&gt; and &lt;h2&gt;respectively as this makes sense with the homepage...) Merge pdfs sequentially I would like to merge 4 pdfs, pdf1.pdf, pdf2.pdf, pdf3.pdf pdf4.pdf together so that the pdfs are spliced, i.e. the first page will be the first page of pdf1, the second the first of pdf2, the third the first of pdf3, etc.  The pdf files are with plain images, no table of contents.  How would I accomplish this? It would be nice to do it from Terminal as well. 'pyrcc4' is not recognized as an internal or external command? C:\Users\Department\.qgis2\python\plugins\np&gt;pyrcc4 -py2 resources.qrc -o resources.py      'pyrcc4' is not recognized as an internal or external command,      operable program or batch file.   How do I solve this problem? 'innerText' works in IE, but not in Firefox I've searched online, but I have not found any clear instructions how to permanently add .sty files to my TeXShop installation. I'm using a Mac with OSX (TeXShop is a mac only program).  What is the best way of doing this? The one comprehensive set of instructions I found .   I've got as far as extracting the files (running LaTeX on the .ins and . dtx files) but after that I don't know what to do. I also don't understand how to update the index of my distribution, and whether there are particular OSX specifics (the instructions are for Windows). After writing the FreeNAS IMG to a 16 GB USB flash drive, I can now only use 938 MB. I used the Win32 Disk Imager tool to write the IMG to the device. Then later, when I inserted the the USB drive into my Windows 7 computer it said that it had to be formatted, because it couldn't read it. I believe this is normal. So I formatted it inside Windows using the format option when prompted. So in Windows Explorer now, 938 MB is reported as capacity of this device.    Also, when i check the properties dialog box I can see the same numbers.    And when I check with diskmgmt.msc I can see there are several volumes I don't recognize and unallocated space of 12.79 GB.    Now, I have another 2 GB USB flash drive with the same problem. It too was used for FreeNAS, and it too has a reported capacity of only 938 MB. I thought it was broken there for a while, until I saw the same problem with this 16 GB model.  I tried using diskpart on the 2 GB model, and I saw that there were several partitions there (list partitions) just like on this one. So I used the clean option to try to wipe it, but that wiped off everything so it's totally useless now. I'm not sure how to rebuild it.  Is this a standard routine, like part of the whole "user experience", that whenever you make a bootable USB falsh drive with FreeNAS, it messes up your device? I am new to FreeNAS, so i wouldn't know. But it sure looks like it. Maybe it is in fact the format operation in Windows that messes things up... I don't know. It's not very nice.  How do I restore the capacity back to 16 GB-ish (14.9 GiB)? Passing parameters to a document I compile most of my documents via Makefiles which take care of the bibliography, indexes, etc. Often I'd like to compile different versions from the same TeX file changing only small things (e.g. a beamer presentation plus a version with the handout option).  Is there any standard mechanism for passing parameters to the TeX file so that I can just type make handout to get the handout version in the above example? Error installing any module What is an undefined reference/unresolved external symbol error and how do I fix it? How does SO's new auto-login feature work? SO and SU just told me I've been logged in. I'm guessing because I'm already logged into my Google account... but how does SO know that? Find $\sum_{n=1}^\infty \frac{n^3}{n!}$. I have to find the sum of the following series:  $$\sum\limits_{n=1}^\infty \frac{n^3}{n!}$$  I know how to prove the convergence of this series, but how do i find the sum. I can't use the properties of derivation or integration of the series, i have to do it using the definition that a series converges iff it's sequence of partial sum converges. Find Oracle JDBC driver in Maven repository How to install hp scanjet 200 in Ubuntu 12.04? Unable to scan with hp scan-jet 200. When I type lsusb command in terminal it shows the scanner details.  I opened the simple scan which displays no scanners found, and x sane image scanners also displays the same error.