Prove that $$\sum^{n}_{k=1} \frac{1}{\sqrt{k}}&gt;\sqrt{n}$$ for all $n\in \mathbb{N}$ where  $n\geq2$. I've already proven the base case for $n=2$, but I don't know how to make the next step.  Is the base case right?  for $n=2$ $$\sum^{2}_{k=1} \frac{1}{\sqrt{k}}=\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}=\frac{\sqrt{2}+2}{2}&gt;\sqrt{2}$$
I am just starting out learning mathematical induction and I got this homework question to prove with induction but I am not managing.  $$\sum\limits_{k=1}^{n}{\frac{1}{\sqrt{k}}\ge\sqrt{n}}$$  Perhaps someone can help me out I don't understand how to move forward from here: $$\sum\limits_{k=1}^{n+1}{\frac{1}{\sqrt{k}}+\frac{1}{\sqrt{n+1}}\ge \sqrt{n+1}}$$ proof and explanation would greatly be appreciated :) Thanks :)  EDIT sorry meant GE not = fixed :)
Why does Gandhi want to nuke me? Different civilizations obviously have different priorities. For example, Gandhi always seems to rush nuke technology and the Mongols will most likely start invading and spread like mad. Are these variables public knowledge? Can you tell by who you are playing what strategy they will adopt during the game? If you have the ability to cast a spell without a spell slot, can you cast that spell using a spell slot? A 10th level Drow warlock (for instance) has the following Drow Magic racial trait (PHB p. 24), in addition to its warlock spellcasting abilities:  You know the dancing lights cantrip. When you reach 3rd level, you can cast the faerie fire spell once per day. When you reach 5th level, you can also cast the darkness spell once per day. Charisma is your spellcasting ability for these spells.  Can the Drow warlock cast faerie fire (which is not on the warlock spell list) using a warlock spell slot? Can it cast darkness (which is on the warlock spell list) using a warlock spell slot?  The  says this about the Magic Initiate feat:  If you’re a spellcaster, can you pick your own class when you gain the Magic Initiate feat? Yes, the feat doesn’t say you can’t. For example, if you’re a wizard and gain the Magic Initiate feat, you can choose wizard and thereby learn two more wizard cantrips and another 1st-level wizard spell. If you have spell slots, can you use them to cast the 1st-level spell you learn with the Magic Initiate feat? Yes, but only if the class you pick for the feat is one of your classes. For example, if you pick sorcerer and you are a sorcerer, the Spellcasting feature for that class tells you that you can use your spell slots to cast the sorcerer spells you know, so you can use your spell slots to cast the 1st-level sorcerer spell you learn from Magic Initiate. Similarly, if you are a wizard and pick that class for the feat, you learn a 1st-level wizard spell, which you could add to your spellbook and subsequently prepare.  But this specifically requires you to pick the feat for one of your classes to be able to cast the spell learnt using your class spell slots, and does not seem directly applicable. A Warlock can use warlock Pact Magic spell slots to cast spells learnt from levels of another spellcasting class, per the multiclass spellcasting rules (PHB p. 164):  If you have both the Spellcasting class feature and the Pact Magic class feature from the warlock class, you can use the spell slots you gain from the Pact Magic feature to cast spells you know or have prepared from classes with the Spellcasting class feature, and you can use the spell slots you gain from the Spellcasting class feature to cast warlock spells you know.  Similarly, if the warlock has learnt the invocation Mask of Many Faces (PHB p. 112)...  You can cast disguise self at will, without expending a spell slot.  ...Can the warlock cast disguise self using a spell slot, e.g. to decrease the chance it can be dispelled? problems with ellipse TikZ I'm working on a mac, I use the package TikZ and it works. But I have problems when I want use ellipse or diamond ex :  \documentclass{article} \usepackage{graphicx} \usepackage{tikz} \begin{document} \begin{tikzpicture} \node[ellipse] {Ellipse}; \end{tikzpicture} \end{document}   If somebody could help me thank you ! Rate limit suggested edits We need a hard rate limit on suggested edits, to limit the damage someone can do with blasting the review queue with minor edit suggestions.  Case in point:  peppered the site with a whopping 133 tag-only edit suggestions in 2 hours and 15 minutes. That's one edit every minute on average, but towards the end he was entering a new suggestion every 20 seconds. He only stopped because a  drew enough rejections to have him banned from entering more.  If there was a limit to the number of suggested edits you can enter in a time period we could have stopped this guy earlier. No &lt;2k user needs to edit hundreds of tags across that many questions in 2 hours time.  Considerations   There are cases where a retag drive or tag burninate justifies editing a larger number of posts, but I'd be fine if such tasks were limited to people with 2k+ reputation. A retag or burninate job requires a minimal engagement with the community to know when they are justified anyway. The suggested edit review process, by itself, was clearly not enough to stop this barrage. It cannot be seen as a rate limiting measure, at least not as a sufficiently efficient one.  The vast majority of the edits made in the above example were too minor, leaving spelling, grammar and formatting mistakes in the post untouched. The user was going too fast to pay attention to such details anyway. Yet this user has 98 approved edit suggestions, but all but 6 or 7 I'd have rejected as too minor, so the review process itself is broken.   What should be limited   The number of review votes reviewers have is already limited; I burned through 20 reviews in short order just reviewing the suggestions from just this one user. Certainly the number of unreviewed suggestions should be limited to let reviewers catch up with a user like this. I'd say having 20 outstanding suggested edits pending review is plenty. Suggested edits should be made with some consideration; we don't want minor edits, so if you are suggesting more than 20 in an hour (that's 1 every 3 minutes) you are not improving posts anymore, you are gaming the system to gain reputation. How is the passage of time handled in Pokemon? Proving set of interiors is open I recently submitted an application to the AppExchange, only to have it not pass the security check due to "Insecure Storage of Sensitive Data Vulnerability." The problem is that my app accesses an external API, for which it has its own API Secret and API Key. These are static, and specific to the Salesforce App- they will be the same for all users, all installations, etc.  Perhaps stupidly, I stored them as private properties of the class that uses them.  private static String apiSecret = 'superS3|&lt;R37'; private static String apiKey = 'sameHerebutdifferent';   It is a Managed app, so users cannot see them. As such, I am puzzled as to 1. why this is insecure and 2. how better to store these values, given that we are apparently operating under the assumption that having them in the text of the class itself is insecure. Icon for pinned tabs in Safari? It would be nice to  for .  As it is, SE kind of stands out (in a not cool way): I had posted a  last week about customizing a ToolValidator class and got some very good answers.  In working with the proposed solutions, I have created a custom module that performs queries on a db, and will be called by both the ToolValidator class (to provide values for the drop-down lists) and later in the geoprocessing script (to get other parameters based on items selected in drop-down lists).  However, I can't seem to actually call the custom module in the ToolValidator class.  I have been trying to append to path with no luck.  When I try to apply these changes to the script, I get a runtime error:  [Errno 9] Bad file descriptor.  If I comment out import line, no errors.  sys.path.append('my_custom_module_directory') import my_custom_module   Many of you may be asking why don't I just implement a custom tool with ArcObjects.  The reason is that my end users don't have the privleges necessary to register ANY dlls on their computer.  UPDATE:  This was happening to me in ArcGIS 10.  Interestingly enough, I was initially appending to the path inside of the initialiazeParameters function of the ToolValidator class.  If I do the append outside (i.e., on top of) of the ToolValidator class, everything works as expected.  sys.path.append('C:/Working/SomeFolder') import somescript --------&gt;THIS WORKS  class ToolValidator:   """Class for validating a tool's parameter values and controlling   the behavior of the tool's dialog."""    def __init__(self):     """Setup arcpy and the list of tool parameters."""     import arcpy     sys.path.append('C:/Working/SomeFolder')     import somescript -------&gt; THIS DOESNT WORK     self.params = arcpy.GetParameterInfo()   UPDATE 2:  I think I found the true cause of my problem.  In the code snippets in this post, I have been appending what appear to be real paths (ex C:/Working/SomeFolder) to the sys.path.  In my actual ToolValidator class, I was constructing a relative path using os.path.dirname(__file__) +"\my_special_folder...".  I was anticipating that os.path.dirname(__file__) would return the path of the toolbox, since that contains the ToolValidator class.  I have come to find this is not the case.  As far as I can tell, the ToolValidator class is never actually written to a .py file, and I speculate the the this code is passed to the python interpreter in memory, so __file__ is useless, or some temp script is persisted and then execfile(path_to_script) is called, again rendering __file__ useless.  I'm sure there are other reasons I am missing as well.    Long story short, if I use a hardcoded path, the sys.append works anywhere, relative paths don't work so well in the ToolValidator class. British Airways (BA) just changed our flight times, leaving us only 1h15mins for our layover in Heathrow. We arrive from Brussels in terminal 5 in Heathrow at 7:55 and our next flight leaves for Miami in Heathrow terminal 3 at 9:10.  This seems awfully short.   Does anyone know whether this is doable?   The flights are in November, so I'm still hoping that the flights will change back to the original flight times, which would give us an additional hour for the layover, but in case this does not happen, what are the chances that we will make the connecting flight in 1h15mins? Using beamer \visible command inside a table, without adding vertical space When using the beamer \visible command inside a tabular environment, beamer adds an extra vertical space before the text. For example, in the following code, beamer adds an empty line before the word World in the second row. Can this be avoided?  \documentclass{beamer} \begin{document} \begin{frame}   \begin{tabular}{|p{1cm}|p{1cm}|}     \hline     1 &amp; Hello World \\     \hline     2 &amp; \visible&lt;2-&gt;{Hello World} \\     \hline   \end{tabular} \end{frame} \end{document} What is the simplest and most robust way to get the user's current location on Android? How can I test the quality of a RNG? On electronics.stackexchange we had  about constructing a True Random Number Generator. Since the method relies on noise, which isn't deterministic, the only way to test the quality of the RNG seems to be empirical. Not being a statistician I suggested to test a long bit sequence for normality, but I have no idea what outcome is acceptable and what isn't. For instance counting single bits I guess we have a thumbs-up for a 499500/500500 distribution, but when is the ratio too much skewed to be acceptable? Same for 2-bit and longer sequences. Of course, if testing for normality is a Bad Idea™, I'd like to hear it, including better alternatives.    edit Diehard was mentioned a few times, but I'm not sure this answers my question. The normality test should give a normal distribution, with better bell curve approximations for longer sequences. Diehard seems also to have tests which either should result in normal or exponential distributions. But my question remains: how do I judge the results? Just by looking at the curve and discern a bell curve in it? To get back at my first example, a 499500/500500 distribution is definitely OK, and a 950000/50000 distribution definitely is a no-no, so where does the switch-over happen? On my Toshiba Encore 8 Tablet I noticed that the CPU usage is very high. In Taskmgr / ProcessExplorer, I can see that OneDriveSetup.exe is hogging 1 CPU cores heavily for hours.    How an I solve this hang and finish the OneDrive Update? What are "Community Wiki" posts? Process substitution and pipe I was wondering how to understand the following:     Piping the stdout of a command into the stdin of another is a powerful   technique. But, what if you need to pipe the stdout of multiple   commands? This is where process substitution comes in.   In other words, can process substitution  do whatever pipe can do?   What can process substitution do, but pipe cannot? how to disable system apps without root? Is there a way to check the size of the video memory? Specifically, is there one that works accurately for both integrated GPU's as well as PCI/AGP graphics cards?  Many integrated GPU's have dynamically allocated memory, so the solution would hopefully return either the maximum available video memory or the currently allocated amount. For stand-alone NVidia or ATI cards it would obviously return the total amount of physical GPU RAM.  lspci -v does output memory figures, but I do not believe it is the video memory. I suspect the figure reported is some system memory allocation or block or channel size, but I don't know for sure. You can see in these  that lspci was wrong in 5 of the 6 tests:  ** ASUS EN210 PCIe - 1024 Mb ***   01:00.0 VGA compatible controller: nVidia Corporation GT218 [GeForce 210] (rev a2)         Subsystem: ASUSTeK Computer Inc. Device 8354         Memory at e3000000 (32-bit, non-prefetchable) [size=16M]         Memory at d0000000 (64-bit, prefetchable) [size=256M]         Memory at e0000000 (64-bit, prefetchable) [size=32M]  *** Galaxy 8400GS PCIe - 512 Mb ***   01:00.0 VGA compatible controller: nVidia Corporation G98 [GeForce 8400 GS] (rev a1)     Subsystem: nVidia Corporation Device 05cc     Region 0: Memory at e4000000 (32-bit, non-prefetchable) [size=16M]     Region 1: Memory at d0000000 (64-bit, prefetchable) [size=256M]     Region 3: Memory at e2000000 (64-bit, non-prefetchable) [size=32M]  *** VirtualBox VM - 10 Mb (headless server) ***   00:02.0 VGA compatible controller: InnoTek Systemberatung GmbH VirtualBox Graphics Adapter         Memory at e0000000 (32-bit, prefetchable) [size=16M]  *** VirtualBox VM - 128 Mb ***   00:02.0 VGA compatible controller: InnoTek Systemberatung GmbH VirtualBox Graphics Adapter (prog-if 00 [VGA Controller])         Memory at e0000000 (32-bit, prefetchable) [size=128M]  *** S3 Savage 4 AGP - unknown Mb (old lspci log), but I don't think they made these cards with 128Mb memory! ***   00:01.0 VGA compatible controller: S3 Inc. Savage 4 (rev 06) (prog-if 00 [VGA controller])     Subsystem: IBM Unknown device 01c5     Region 0: Memory at feb80000 (32-bit, non-prefetchable) [size=512K]     Region 1: Memory at f0000000 (32-bit, prefetchable) [size=128M]  *** NVIDIA Quadro FX 1800 integrated - 1024 Mb ***   01:00.0 VGA compatible controller: nVidia Corporation GT215 [Quadro FX 1800M] (rev a2) (prog-if 00 [VGA controller])     Subsystem: Dell Device 040c     Memory at e2000000 (32-bit, non-prefetchable) [size=16M]     Memory at d0000000 (64-bit, prefetchable) [size=256M]     Memory at e0000000 (64-bit, prefetchable) [size=32M] Command-line mv exclusion list Error in batch file to copy folder: 'Invalid number of parameters' I am making a batch file in Windows XP to copy my folders I need to another folder on my PC. I am getting an error.  I get the error "Invalid number of parameters".  xcopy /s/z D:\Documents and Settings\%username%\Desktop C:\SomeRandomFolder\ xcopy /s/z D:\Documents and Settings\%username%\Favorites C:\SomeRandomFolder\ xcopy /s/z D:\Documents and Settings\%username%\Start Menu C:\SomeRandomFolder\ xcopy /s/z D:\Documents and Settings\%username%\My Documents C:\SomeRandomFolder\ xcopy /s/z D:\Documents and Settings\%username%\PrintHood C:\SomeRandomFolder\ xcopy /s/z D:\Documents and Settings\%username%\NetHood C:\SomeRandomFolder\ xcopy /s/z D:\Documents and Settings\%username%\Templates C:\SomeRandomFolder\ xcopy /s/z D:\Documents and Settings\%username%\Searches C:\SomeRandomFolder\ xcopy /s/z D:\Documents and Settings\%username%\Local Settings\Application Data\Microsoft\Outlook C:\SomeRandomFolder\ pause   Then I changed the batch and get this error: "File not found - Desktop"   xcopy /s/z D:\...\%username%\Desktop C:\SomeRandomFolder\ pause   How do I fix these errors?