Need a hint to start prove an inequality
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
What is a decoupling capacitor and how do I know if I need one? What is a decoupling capacitor (or smoothing capacitor as referred to in the link below)?  How do I know if I need one and if so, what size and where it needs to go?    mentions many chips needing one between VCC and GND; how do I know if a specific chip is one?   Would an  4-bit parallel access shift register used with an Arduino need one? (To use my current project as an example) Why or why not?  I feel like I'm starting to understand the basics of resistors and some places they're used, what values should be used in said places, etc, and I'd like to understand capacitors at the basic level as well. Why Doesn't a Bootable USB Boot How to disable battery charging? From the pmset man page:     POWER SOURCE ARGUMENTS      -g with a 'batt' or 'ps' argument will show the state of all attached power sources.      […] Certain Apple battery calibration tools may temporarily disable   battery charging, even though your Apple portable is plugged into AC   power.      Such tools will never surprise you with this behavior; you will know   it's happening. This state will be reflected in an additional line of   output to 'batt' or 'ps' readings, including the pid of the app   inducing this behavior.       'ChargeInhibit':    1432    So, does any piece of publicly available software exist to force the battery not to charge? Where does "wicked" get its /ɪd/ from? There are three ways I know to pronounce the -ed at the end of an adjective:   /t/ as in cracked. /d/ as in lined. /ɪd/ as in naked   I realise naked is a special case because, as , it comes for Old English nacod, so the suffix isn't added.   shows the pattern of pronunciation of -ed in all other cases. However it doesn't explain why  ends with /ɪd/ (or /id/ or /əd/ depending on the dialect).   that wicked comes from OE wicca, so the d wasn't already there.  Why do we pronounce wicked as /ˈwɪkɪd/ and not /ˈwɪkt/? What the matter is vs. what is the matter used in the affirmative I want to know what the matter is with her.  I want to know what's the matter with her. I want to know what's her problem.   Is "I want to know what's the matter with her" and 'what's the matter'  incorrect as Cambridge dictionary suggests (). In their explanation it is suggested that the word 'matter' be replaced with 'problem' as is written in the 3rd example.    Thanks for whatever help you can provide on this.  I've read Rathony's link and agree that his link answered the question about inversion. Now my question is specifically about the correctness of using this wording and if it is correct is there a rule in its usage. What lubricants can be safely added to a laptop fan? I've got a fan in a laptop that occasionally makes some loud airplane-like noises.  It mostly happens about 10 seconds after booting up and lasts for 10-20 seconds.  It also occasionally happens when the computer is running, but very rarely.  Interestingly, it does not seem to happen when the processor is being used heavily.  The laptop does not have a discrete graphics card.  The fan is clean.  I'm not sure if the laptop is under warranty, but I trust my own skills much more than I trust the manufacturer (or the shipper).  Before I search for a matching fan and replace it, I thought I would see if it is safe to try any lubricants.  Are there any lubricants that are safe to use inside a laptop?  I don't want a fire or anything that will splatter and cause conductivity issues within the circuitry. Make it clearer when looking at a question if I've already voted to close it Since "" we now have the possibility to retract close votes.   However, as mentioned in "" there is no indication when looking at a question to see if I have already cast such a close vote.  Therefore, could we have a UI improvement to show this? Adding some image with freehand circles to improve visibility. $\lim_{n→∞} f(n+x)=0$ results in $ \lim_{x→∞} f(x)=0$ $f\colon [0,\infty) \to \mathbb{R}$ is uniformly continuous.  If $\lim_{n\to \infty}f(n+x)=0$ where $x\in [0,1]$, then $\lim_{x\to\infty} f(x)=0$.  every my trying to solve this is wrong :(  how can i prove this?  and if $f$ is just continuous, what happens to the results Does it make sense to get a PhD if a person does not want to be in academia and prefers to stay in business? Compression API on the iPhone If an enemy is just below a 10-foot-high ceiling, are they in melee range of a creature on the ground? I need to start reading Lucifer comics, but I am having trouble figuring out where to start Do I read the Sandman stuff, or do I jump right into the main comics? Because I really want to maintain continuity, what's the right sequence to ensure that I get every bit of the story? Getting text from last marker to EOF in POSIX.2 Let $f:A\rightarrow B$ and $C\subset B,D\subset B$. Prove that $f^{-1}(C\backslash D)=f^{-1}(C)\backslash f^{-1}(D)$ After reinstalling TeXLive distribution (install-tl-20160318, Ubuntu 14.04), a issue occurs with the updated version of the titlesec package: the section numbering is lost.  What could it be missing? Is there a modification I have not seen?  Below is a MWE comparison of the two versions. The prevtitlesec package is a reinstall of the previous version (2011/12/15).  \documentclass{book} \usepackage[margin=2cm,a4paper]{geometry} %\usepackage{prevtitlesec}% 2011/12/15 version \usepackage{titlesec}% 2016/03/15 version \usepackage{lipsum}  \begin{document}  \chapter{Title of the first chapter} \lipsum[1] \section{A test section} \lipsum[4] \subsection{A test subsection} \lipsum[4] \subsection{A test subsection} \lipsum[4]  \end{document}   titlesec package 2011/12/15:    titlesec package 2016/03/15: I have some kind of test data and want to create a unit test for each item. My first idea was to do it like this: import unittest  l = [[&quot;foo&quot;, &quot;a&quot;, &quot;a&quot;,], [&quot;bar&quot;, &quot;a&quot;, &quot;b&quot;], [&quot;lee&quot;, &quot;b&quot;, &quot;b&quot;]]  class TestSequence(unittest.TestCase):     def testsample(self):         for name, a,b in l:             print &quot;test&quot;, name             self.assertEqual(a,b)  if __name__ == '__main__':     unittest.main()  The downside of this is that it handles all data in one test. I would like to generate one test for each item on the fly. Any suggestions? Is this noun used as an adjective? I read this recently in :     At the end of the summit, the French and European officials had   claimed a points victory over the Germans by getting them to agree   more firmly to a target date of January 1st next year to entrust the   European Central Bank (ECB) with the ultimate authority to supervise   the euro zone’s 6,000-odd banks.   "Points" is a plural, and I suppose it doesn't function as a noun in this sentence since it's following the article "a", so is it an adjective adorning "victory"? Is there a catch-all place on the Stack Exchange network where one can post any question that does not obviously belong to the Stack Exchange sites? Is there a catch-all place somewhere on the Stack Exchange sites where one can post a (any) question that does not obviously belong to any of the Stack Exchange sites?  Sometimes I have questions but I don't want to ask them on other sites (no need for names). I prefer to post it on the Stack Exchange network for various reasons.  If there isn't, are there plans for one? I imagine that if such a site exists, questions on that site can also be moved to other more specific sites when they exists, and it's not to be used to post questions which obviously belong to a specific Stack Exchange site. Change \textwidth after first page in scrlttr2 WoeUSB Error Code 256 with NTFS formatted USB