HP windows 10 keeps saying restarting
Computer keeps restarting by itself
Proving an inequality by induction, how to figure out intermediate inductive steps? I'm working on proving the following statement using induction:  $$ \sum_{r=1}^n \frac{1}{r^2} \le \frac{2n}{n+1} $$  Fair enough. I'll start with the basis step:  Basis Step: (n=1) $$ \sum_{r=1}^n \frac{1}{r^2} \le \frac{2n}{n+1} $$ $$ \frac{1}{1^2} \le \frac{2}{1+1} $$ $$ 1 \le 1  \checkmark  $$  Inductive Step: $$ \sum_{r=1}^{n+1} \frac{1}{r^2} \le \frac{2(n+1)}{(n+1)+1} $$ $$ \sum_{r=1}^{n+1} \frac{1}{r^2} \le \frac{2(n+1)}{n+2} $$  My goal is to prove $\forall_{n\ge1} s(n) \implies s(n+1) $ or that this inequality holds true for all $n\ge1$.  I'm not quite sure to go from here on the inductive step. I understand that I need to basically work some clever substitution and manipulation into the problem to end up with: $$ \sum_{r=1}^{n+1} \frac{1}{r^2} \le \frac{2n}{n+1} $$  However, I'm not quite sure what needs to done to obtain this after attempting a few times. canonical-livepatch, Doesn't seem to patch anything Automatically show which tags were edited in revision history I’ve developed the habit of using the revision summary to indicate which changes I’ve made to the tags while retagging a question.  For instance, if the question originally had tags   and it should be  instead, I write the following in the revision summary:     Edited tags: -cocoa, -touch, +cocoa-touch   which I find useful (and potentially educational) for the OP and other editors.  On the other hand, when an editor doesn’t type a revision summary, Stack Overflow shows     User (timestamp) edited tags   with no indication of the difference between previous tags and the tags set by that edit.  Since there’s a limit on the number of tags, this difference would easily fit in the revision history list of that question. Could this be automatic in case the editor doesn’t fill the revision summary? Is it worth it? I want to select the value from the dropdown I am testing www.paytm.com  In that I have filled in the mobile number but I am not able to focus and select the mobile operator which is present in the dropdown just after the phone number section.  I want to select 'vodafone' as the value from the dropdown.  How to do that using webdriver  Code I have written till now  `  public class MMT {   public static void main (String[] args)  {  System.setProperty("webdriver.chrome.driver","E:/som/chromedriver/chromedriver.exe");  WebDriver driver = new ChromeDriver();  driver.get("http://paytm.com");  driver.findElement(By.id("mobile-number")).sendKeys("9876543212");`   What should be my next steps? I can't play Pokemon GO! What's wrong? What are some good introductions to philosophy? I've been searching the questions posed here, and don't seem to find one that gives the answers I am looking for. I've proposed to start a  on meta but no one proposed anything, so I feel I must ask this question: What are some books generally regarded as good for a general introduction on philosophy? By this I mean good books that can introduce you to philosophy in general and throughout the times, not to some philosophy or period in particular.   almost answers mine, except for the fact that most things proposed there are not books, thus not giving me much options to weigh upon.  regards contemporary philosophy in particular. And  has the same problem as the first one, plus the fact that it asks for layman's terms, which is not what I am looking for.  I've been tempted to buy Will Durant's , but am not sure if it is the best book to get started on philosophy (plus, the book has some mixed reviews). I also checked , which seems to be unanimously good, but has the format of dictionary/encyclopaedia, which is not exactly what I am looking for (at least as a main source).  also seems to be a good introduction regarding how to do philosophy, rather than to its history and ideals (this also interests me, but I'd rather learn about the philosophers and their theories first).   It is also important to point out that I have little notions (or none at all) on philosophy. I would like to read something that covers from classical to contemporary philosophy generally (although I do not know if there is such a book), so that from there I could pick some author, period or branch of philosophy in particular to read further on. So, to sum up, I would like to 'hear' your opinions on what are some books generally regarded as good for a general introduction on philosophy. How to prevent US post code formats I have an issue with American and Canada postcodes in accounts and contacts. Some of the users are creating the salesforce records with postcodes like (MD 20904), when we sending post code from salesforce to SAP integration, SAP system is rejecting salesforce records as postcode is not in correct format.   My question is:   what are actual US and canada post code formats? If Users are creating the post codes with MD 20904, how would prevent through validation rule like only accept sepecific format? $x^y = y^x$ for integers $x$ and $y$ How can I get bash to perform tab-completion for my aliases? I have a bunch of bash completion scripts set up (mostly using bash-it and some manually setup).    I also have a bunch of aliases setup for common tasks like gco for git checkout. Right now I can type git checkout dTab and develop is completed for me but when I type gco dTab it does not complete.    I'm assuming this is because the completion script is completing on git and it fails to see gco.    Is there a way to generically/programmatically get all of my completion scripts to work with my aliases?  Not being able to complete when using the alias kind of defeats the purpose of the alias. Order posts by tags count? I am trying to order posts by tag count. I want to order posts with no tags first and posts with highest count last.  I tried and got posts with no tags only.       $tags = get_tags();     $tag_ids = wp_list_pluck( $tags, 'term_id' );      $args1 = array (        'orderby'          =&gt; 'DEC',        'post_type'        =&gt; 'post',        'pagination'       =&gt; true,        'posts_per_page'   =&gt; '1',        'tag__not_in'      =&gt;  $tag_ids,        'meta_key'         =&gt; '_thumbnail_id',     );   How do I order posts based on the tags count? How to increase difficulty in Dungeon World I've been GMing for a couple of sessions now and I'm still struggling at making encounters or situations more difficult. I will describe dangerous situations and encounters in fiction but the mechanics make it too easy for my players to succeed.  For instance no matter how big I describe the Troll, if the fighter of the party charges him and swing his sword, roll+2 for Hack and slash, he'll easily hit the troll. Almost 40% chance to hit without consequences. Why does the right leg's bone in my rig move when I move the left? For some reason, when I moved the left leg's bone, the right leg has also moved and the bone of the right leg doesn't control anything at all.  I think this is because I used Mirror to make the model, but I'm not sure I'm a complete beginner. Are groups satisfying $g=g^{-1}$ for all $g \in G$ abelian? Is the following statement true or false:  If $G$ is a group with the property that $g=g^{-1}$ for all $g \in G$, then $G$ is abelian.   I believe it is false since I know that abelian or commutative property implies that every element in $G$ must have an inverse. Thus $g\cdot g^{-1}= g^{1}\cdot g = e$. I need someone to check my attempt. Determinant of a square matrix in a field \begin{array}{rrrrr|r}     b &amp; a &amp; a &amp; \cdot \cdot \cdot &amp; a \\     a &amp; b &amp; a &amp; \cdot \cdot \cdot &amp; a \\     a &amp; a &amp; b &amp; \cdot \cdot \cdot &amp; a \\     \cdot &amp; \cdot &amp; \cdot &amp; \space &amp; \cdot\\ \cdot &amp; \cdot &amp; \cdot &amp; \space &amp; \cdot\\ a &amp; a &amp; a &amp; \cdot \cdot  \cdot &amp; b   \end{array}  I have the above matrix $A\in M_{n\times n}(F)$ where $F$ is a field and $n\geq1$, $a,b\in F$.  I'm trying to find out how to use row operations to make it into an upper triangular matrix in order to figure out the determinant. But I'm not sure how I would approach it. How to run an encrypted virtual machine? Windows 7 + Deep Freeze - I'm stuck in an endless reboot loop I have the following setup:   Windows 7 Ultimate Deep Freeze   I "thawed" my machine last night and performed a Windows Update. The update is having issues (it gets stuck at 32%, fails, and restarts my machine). When it reboots it attempts it again, and again, and again, etc. (Endless loop).  I looked online and found some solutions, but none of them seem to be working:   When I run Safe Mode, Safe Mode w/ Network, or Safe Mode w/ Command Prompt it attempts to revert the Windows Update changes. However, the problem is with Deep Freeze on (and now in "Frozen" mode) the reverted changes don't stay, and I'm back into the loop of death. Oh, and side note: "Safe Mode w/ Command Prompt" does not actually take me to a command prompt window? Perhaps because it is attempting to complete the Windows Update changes first? I have tried to select the option to NOT restart when an windows error occurs, but it still does. I tried the remainder of all the other options in the F8 screen.     The only other option left is to find my Windows 7 Media Disc (I can't find it right now) and use it to repair windows (because for some reason the repair option does not show up in the F8 screen).  Is there a way to disable Deep Freeze from loading? When I selected "Safe Mode w/ Command Prompt" I noticed that it loads the DpFrz.sys file. I know that when I'm in the Windows Boot Manager if I press F10 instead of F8 (while highlighting Windows 7) it takes me to an "Edit Boot Options" screen:     Edit Windows boot options for: Windows 7      Path: \Windows\system32\winload.exe      Partition: 2 Hard Disk: 8e90e329      [ /NOEXECUTE=OPTIN (I CAN EDIT THIS LINE)   ]     Update: I found my Windows 7 Media Disk and it did not help out. The laptop had the "System Restore" as a partition on the HDD. I later received (in the mail) a Windows 7 Upgrade Disc from Sony to upgrade my system from Windows Vista to Windows 7 Ultimate. I placed the disc into the DVD drive and it does not come up as a "bootable" disc. I'm going to try to find an alternative disc to see if I can get into Command Prompt.    Update 2: I got a Windows Repair disc and got into a command prompt window. I got into the registry and disabled Deep Freeze. Also:   I renamed the Pending.xml file to Pending.old I cleared out the Windows Temp directory   I still am stuck in the loop (though, it isn't an issue with DeepFreeze anymore because I can make changes to the hard drive and they persist). Not sure what to do at this point?    Update 3: I ran the repair option and it couldn't repair, but it did point me to something. It says the error was due to a driver that was failing. I have a feeling it is my UPEK Fingerprint scanner. If $\mid a_{jj}\mid \gt \sum_{i \neq j} \mid a_{ij} \mid$ then vectors $a_1,\dots ,a_n \in \mathbb{R}^n$ are linearly indendent. Let $a_1,\dots ,a_n \in \mathbb{R}^n$ with $a_i = (a_{i1}, \dots , a_{in})$.  Show that when $\mid a_{jj}\mid \gt \sum_{i \neq j} \mid a_{ij} \mid \; \forall \; j\in \{1,\dots ,n\}$, then $a_1,\dots ,a_n$ are linearly independent.  I want to show that the matrix \begin{matrix} a_{11} &amp; a_{21} &amp; \cdots &amp; a_{n1} \\ a_{12} &amp; a_{22} &amp; \cdots &amp; a_{n2} \\ \vdots &amp; &amp; \ddots &amp; \\ a_{1n} &amp; a_{2n} &amp; \cdots &amp; a_{nn} \end{matrix} can be transformed into an upper triangular matrix with all entries in the main diagonal $\neq 0$.  For the cases $n=1$ and $n=2$ this is easy. However, I fail to show this for the general case; the problem being that the tranformations mess up the coefficients such that I can't use the assumption on the $a_{jj}$'s anymore.  I'm pretty sure that this has already been solved somewhere on here, but I don't know how to search for it. Can there be two distinct, continuous functions that are equal at all rationals? Akhil showed that the  is the same as the continuum, using as a step the observation that continuous functions that agree at rational points must agree everywhere, since the rationals are dense in the reals.  This isn't an obvious step, so why is it true? I have a vf page that is a custom button. That's it.  this VF page is on a STD Page Layout. When the user clicks on the VF page, the parent window needs to be redirected to the new URL.  The way this is working, is that the new page is opening in the vf section of the page layout.   &lt;apex:page standardController="Opportunity"  standardStylesheets="true" extensions="OpportunityController" &gt; &lt;base target="_parent" /&gt; &lt;body style="background:#f3f3ec" &gt; &lt;apex:form &gt; &lt;center&gt;  &lt;apex:commandButton action="{!redirect}"  value="Change Record Type" rendered="{!render}"/&gt; &lt;/center&gt;   &lt;/apex:form&gt;    &lt;/body&gt; &lt;/apex:page&gt; Math Induction Proof: $(1+\frac1n)^n < n$ So I have to prove:      For each natural number greater than or equal to 3,   $$(1+\frac1n)^n&lt;n$$   My work: Basis step: $n=3$ $$\left(1+\frac13\right)^3&lt;3$$ $$\left(\frac43\right)^3&lt;3$$ $$\left(\frac{64}{27}\right)&lt;3$$ which is true.  Now the inductive step, assume $P(k)=\left(1+\frac1k\right)^k&lt;k$ to be true and prove $P(k+1)=\left(1+\frac1{k+1}\right)^{k+1}&lt;k+1$.   This is where I am stuck because usually you add or multiply by $k+1$ or some similar term.