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I have put his on wolfram and obtained answer as follows:  $\sum_{n=1}^{\infty}\frac{n}{2^n} = 2$  And the series is convergent too because $\lim_{n\to\infty} \frac {n}{2^n} = 0$  However I am wondering if there is a convenient way to solve this; I don't think you can represent it by a geometric progression either. So how do we have to do it on paper? How do I install additional drivers? I've just installed Ubuntu and I need either video, wireless, or some sort of other manufacturer (non-opensource) driver. How can I run the tool that will fetch all of these for me? I'd like graphical instructions.  Related: Dump of my own Stack Exchange content Is there a way to quickly save all my Stack Exchange content across all Stack Exchange sites, as hundreds of HTML pages? (for me probably 15 or 20 sites: SO, dsp.SE, unix.SE, etc.)?  The ideal way would be one .HTML file for each question that I asked / answered / commented? What would be the ideal tool for that?    Remark: I've already read interesting questions like  but it doesn't exactly answer my concern here. A guide to moderating chat Chat is an offshoot of the main site, and using it is  during their time here.  Chat is our place for:        Real-time collaboration   Meeting fellow members of the community   Less structured, casual (but still roughly on-topic) conversation      Our chat system exists to serve the main site; users of each site can gather and commune with each other.  When in chat, we expect all users to abide by our  policy, which means that we expect community members to treat each other with respect.    While it is a place where the community can go to interact on a more casual level, chat still needs to be moderated by the community and there are tools in place to help with the moderation. This raises a few questions, that are addressed here: A friend of mine misplaced his passport while staying in Jeju island. Normally I would advise him to just travel to Seoul, get an emergency passport from his embassy and fly back home without issues, but I know that Jeju island has a special immigration regime.   Are there any immigration checks on the way from Jeju island to Seoul? If not, can one travel that route without a passport? How do I upgrade to the unreleased version of Ubuntu for testing? I am creating a controller for a 12 V system using an Arduino Uno microcrontroller. For the outputs I am using a relay shield to switch the 12 V components. I have a 12 V toggle switch that turns on some 12 V components in the system and I want to use a trigger signal off of this same switch to send to an Arduino digital input. I know that the Arduino can only handle 5 V max. What would be the best way to step down the 12 V coming off of the switch to the 5 V for the input?  EDIT: The system is for use in a car. Would the amperage of the car battery need to be lowered somehow as to not blow up the components? Prove or disprove: $S_{10} = \langle (1,3),(1,2, ... ,10) \rangle$ How much longer will my 10 year old frame last? Time traveler asks archaeologist for help in transporting a girl from dinosaur Earth to present day Many decades ago, I read a short story about a time traveler who asks an archaeologist for help.  He convinces the archaeologist that he can time travel by bringing him back a freshly killed dinosaur (small one.)  The time traveler needs help because when traveling back in time to the age of the dinosaurs he met a girl and wants to transport her back to the present.  However only one person can travel in time at a time so he needs the archaeologist at the other end to wait for the girl.  The archaeologist agrees to help.  Unfortunately after the traveler goes back he and the girl find themselves in the middle of a battle between aliens on Earth.  They are chased by a dinosaur and never make it back to the present.  The archaeologist meanwhile is digging for evidence that the traveler went back in time and the story or my recollection of it ends with that. The new 17.10 only has 64 bit ISOs. However 32 bit is still supported, there just are no live ISOs for it.  I have a 32 bit machine with WIFI, and I need to install from a USB disk. I tried the "mini.iso" but it doesn't have WIFI support.  What options do I have?  (PS I don't want another distro, and I can't use ethernet for installation, must be WIFI). Possible cardinality of power sets What cardinals can provably not occur as the cardinality of a power set? I know that $\mathbb N$ and natural numbers that are not powers of two are such cardinals. What else is out there? Word caption style -- different style for label and number? This should be a common problem for anyone involved in technical writing.  When you insert an image (or table etc.) caption in Word, you get  dialog. You enter your caption,  "A happy bicycle" (in yellow).  This might be fine for a happy bicycle, but I want to have captions that have one style for the "enumeration" (label and number) and one style for the description (caption text, as called by Word), as such:    I have tried searching for this but I haven't found anything yet... Convert a javascript associative array into json object using stringify and vice versa I found the following blog title without a question mark from :     How to ease Afghanistan’s progress in cricket   Is it grammatical, if we don't put question mark in questions of titles? I think this blog title should have been like this:     How to ease Afghanistan’s progress in cricket?   I also found the following blog title from  without a question mark:     Election rigging 101: How to steal a mandate   However, I found a question mark from other blog title of :     Elections 101: What is the ECP and what does it do on election day? Every $R$-module is a quotient of a free module I'm reading through my notes, and I have a theorem as the title says. As proof I have only a picture.    where $v:m\mapsto(0,...,0,1,0,...,0)$ and 1 is at $m$-th position. I know, that $\oplus_M R$ is a free module generated by set  $M$, but is this all? I do not see how the statement is proved. Title of novel with girl who can read minds by observing body language, later communicates with a hive mind on an alien planet's surface As a kid I was greatly influenced by a book where a girl (I believe her name was Marlena) lived in a ship orbiting an alien planet.  The ship was intended to colonize the planet but the humans had encountered difficulty.  People on the surface early on had gone incurably mad.  The planet was covered with single cell organism, but no other life.  Other than the "bacteria" it was sterile.    The girl, along with most of the colonists, was still living on the orbiting ship for the foreseeable future.  The girl had an uncanny knack of reading people's minds by noting minute changes in behavior and body language, kind of like Sherlock Holmes' famous observations.  Eventually she got a chance to go to the surface, and found the planet trying to communicate with her.  In one memorable scene the swirls in the water of a stream formed a face and started trying to call her name, "Eeeena, Aaleeena, Aarleena, Marlena!"  It turns out that the single celled organisms on the planet comprised a hive mind which had tried to communicate telepathically with previous humans by altering their brains slightly, causing the madness.  The girls's brain was different, however, constantly modifying and changing itself so that it was not damaged by the hive mind's attempts to communicate with it. Selling a car with a lien I own a car personally, but it is mortgaged to a bank. I want to sell it to an individual. I haven't the funds to repay the loan until I'm paid for the car. The buyer doesn't want to pay me without a lien release (or guarantee that one is coming). The bank won't release the lien until it gets the funds. What do people do in a case like this? It must be a common case. What should I do? I had opened a terminal to install macchanger via sudo apt-get install -y macchanger, and then entered my password. It stated that macchanger was already the newest version, so I typed clear and then ran:  sudo ifconfig eth0 down   which is when this error message appeared:  eth0 ERROR while getting interface flags: no such device   This is a laptop and I am connected via ethernet cable.  How can I resolve this, so that I can run macchanger?    So I used ifconfig -a and I'm looking but seeing no mention of  eth0  The interfaces that are showing top to bottom are:  enp58s0f1 lo tun0 UNSPEC wlp59s0   The only reference to ethernet is the MAC and also txqueuelen   Does this help in figuring what I need to do to get this sorted? Closed-form of $\int_0^1 \operatorname{Li}_p(x) \, dx$