In our sequence and series class, my teacher wrote this series and asked if it makes any sense. We all were saying "this makes no sense at all." But when I Googled it, the whole world knows it. So what exactly this series define? Some say string theory uses this series. Can someone explain it?
$\displaystyle\sum_{n=1}^\infty \frac{1}{n^s}$ only converges to $\zeta(s)$ if $\text{Re}(s) &gt; 1$.  Why should analytically continuing to $\zeta(-1)$ give the right answer?
To explain the expansion of space I have often heard people saying that space is continuously created. This picture is usually applied to cosmological scales but I`m nevertheless curious if some microscopic description of this process could be found (or probably is already available?).  The first thing which comes into my mind by thinking about this is that in theories like loop quantum gravity, there is an idea that space is quantized. Would space expansion then be explained as the creation of new quanta in loop quantum cosmology? Or are there other different ideas, such as the quanta themselves changing properties? Do people actually working on this already have some interesting results? A thought experiment: Imagine the Sun is suddenly removed. We wouldn't notice a difference for 8 minutes, because that's how long light takes to get from the Sun's surface to Earth.   However, what about the Sun's gravitational effect? If gravity propagates at the speed of light, for 8 minutes the Earth will continue to follow an orbit around nothing. If however, gravity is due to a distortion of spacetime, this distortion will cease to exist as soon as the mass is removed, thus the Earth will leave through the orbit tangent, so we could observe the Sun's disappearance more quickly.  What is the state of the research around such a thought experiment? Can this be inferred from observation? This looks a little bit like a variation on  but specific to the tags view.  Reproduction (app version 1.0.71):   Select any site (say Meta) from the sidebar Switch to the tags view using the top bar Choose a tag, any tag ( is nice)   optionaly refine your search with more terms  Go to any question found, go back   you end on the unfiltered tags view  Go back again   lucky you, your search is here Hiding reputation and encouraging thinking time would improve the quality of answers on SO I've only been a member of SO for a couple of months but I must say that the site can be a bit daunting even for an experienced developer.  Part of this is because when users with very high reputations answer questions then it seems that everyone assumes that they have the right answer.  I don't want to go into the self-fulfilling nature of reputation increase for high reputation people.  But I think it is clear that people with high reputation scores get more upvotes () because people assume (usually accurately) that they are correct.    But if reputation was hidden on SO, at least for, say, the first hour after a question is asked then the probability of the best answer being upvoted the most would surely increase.  This might also require the hiding of the names of the answerers if they have very high reps!  As a second method of getting improved answers I would correlate the value of an answer (in terms of reputation gained) with the difficulty of the question.  And the simplest way to do that would be based on the time required for the question to be answered.  So if a question is answered within a minute then it is a 20% question (2 points per upvote), within 2 minutes a 40% question, within 5 minutes a 60% question and so on, on to say a 200% answer (20 points per upvote) on questions that have been hanging around for months.  This would encourage considered answers to new questions and tempt people into reducing the backlog - rather than encouraging people to sit on the 'newest questions' hoping for a gimme.  These two measures would incentivise people to answer the questions that no-one likes the look of and reduce the relative value of answering easy questions. I am new to this and not sure what to make of all the options available. I am interested in putting a machine-learning-related preprint, which will potentially be submitted to places like NIPS/ICLR/ICML in the future.   arXiv.org perpetual, non-exclusive license to distribute this article (Minimal rights required by arXiv.org)  Creative Commons Attribution license (CC BY 4.0)  Creative Commons Attribution-ShareAlike license (CC BY-SA 4.0)  Creative Commons Attribution-Noncommercial-ShareAlike license (CC BY-NC-SA 4.0)  Creative Commons Public Domain Declaration (CC0 1.0) Short story about survivors on Earth after the atmosphere has frozen How to visualize a value resulted from math node,or just to know it. I tried the way of scaling this value to the scene size and then pick the color and get the value but I want more effective way to do this. Why wave theory cannot explain photoelectric effect and provides evidence for particle nature of light? Sign of the vector (especially $g$) while calculating I'm a high school student and I'm studying Newton's second Law. While my teacher is calculating a net force of an object he always treat all vectors as positive numbers. I think what he meant is the magnitude of the vector which is always positive, but the problem is that he didn't use the magnitude symbol, for example like $||Fg||$. He said the acceleration due to gravity , g, is positive, but shouldn't it be negative since it is pointing down. This also cause a problem: every time when I calculate the net force I can't add all forces together, instead I need to choose to use minus sign when the vector is pointing down. So in general which way is correct? How to prevent alt-f1 from selecting Dash Circuit tester trips new GFCI I replaced a non-protected receptacle with a GFCI type and now my circuit tester trips the GFCI as soon as it is plugged in.  The receptacle tested fine before replacement, ground, neutral, hot, etc.  I've double checked the hot/neutral/ground connections.  I've also tried it with the downstream load disconnected.   The GFCI trips the moment I plug in my circuit tester (before pushing the test button).  Otherwise things check out OK.  I can plug in a power tool without it tripping.  Also, the integrated test/reset button work correctly.   I've read that the integrated test button is the only one that truly matters. Is this correct or should I be concerned? I'm sure a home inspector will red flag this if their tester has the same result.  Update  My tester is by "Commercial Electric".  The tester is one of the palm sized three prong type with three leds to indicate the condition of the circuit and a button on top to test GFCI. It's new from the local box store. I am an Indian citizen studying in Italy on an Italian visa that expires 19 November, 2015. I have permesso di soggiorno. I want to visit the United Kingdom for my vacations for a week during March. I know the procedures already, however I am a little bit confused about the amount that I must show as a proof of support with my bank statements. I will stay for a week with my friends who are also students in Italy and will be in London for 5 days. What would be the amount in Euros that I need to show for my visit to UK? How to create a file system as a non root user? I'd like to create a filesystem image as a non-root user, the problem I'm facing is that the way I'm currently doing it, it needs a mount and as a non-root can't do a mount.  This is what I'm now doing:  #!/bin/sh  IMG="app.ext4" LBL="PIHU_APP" MNT="/mnt/PIHU_APP" APP="/home/buildroot/board/arctura/PIHU_APP/application"  #64MB: dd if=/dev/zero of=$IMG bs=4096 count=16384  mkfs.ext4 $IMG e2label $IMG $LBL  mkdir -p $MNT mount -o loop $IMG $MNT cp -r $APP $MNT sync umount $MNT   I have full root access, so I can setup/prepare anything, but the script will be executed from a non-root account.  However, I have a feeling there may be a better way that might not even need mounting, but I'm not sure.. How does one get started with web test automation using Selenium? So I've been testing web based analytical software now for the past 4 years or so with mostly manual techniques. But for 2015, I've set myself the goal of getting setup and start writing automated tests and to introduce automated testing into my company.  I've done a little research and it seems that Selenium is quite big when it comes to writing automated tests, but most of the tutorials I've come across reference the Java language.  Some questions:   Is Java the primary language used for Selenium tests?  Do you recommend it over C# ?  Wat is the process of writing test scripts?  Are there Frameworks that I should use that can make the process even easier? How do I report a bug? I found a problem with an application on Ubuntu.   Questions :   How do I best report the issue?  What sort of information should I provide? Integration of $\int\frac{1}{x^{4}+1}\mathrm dx$ Poisson Distribution of sum of two random independent variables $X$, $Y$ $X \sim \mathcal{P}( \lambda) $ and $Y \sim \mathcal{P}( \mu)$ meaning that $X$ and $Y$ are Poisson distributions. What is the probability distribution law of $X + Y$. I know it is $X+Y \sim \mathcal{P}( \lambda + \mu)$ but I don't understand how to derive it. How to Execute ShortCut From Command line in Windows 7 We came with a scenario where we have to use Shortcut file (.lnk), which is on the desktop, to execute an application for a headless device (i.e, without manual intervention).  Is there any way to execute it from Command prompt? How do I check if an element is hidden in jQuery? Is it possible to toggle the visibility of an element, using the functions .hide(), .show() or .toggle()?  How would you test if an element is visible or hidden? Variable scoping in Module