How do I activate WindowsXP now that support has ended?
XP Activation and Dual Booting
Ubuntu 14.04: very slow UI in Oracle VirtualBox Short summary: 14.04 is much slower than 12.04 even with more RAM assigned.  I'm using latest VirtualBox 4.3.10 on Mavericks 10.9.2. How can I make it faster? Prove that $371\cdots 1$ is not prime Prove that $371\cdots 1$ is not prime.   I tried mathematical induction in order to prove this, but I am stuck.  My partial answer:  To be proved is that $37\underbrace{111\cdots 1}_{n\text{ ones}}$ is never prime for $n\geq 1$. Let $P(n)$ be the statement that $37\underbrace{111\cdots 1}_{n\text{ enen}}$ is not prime.  For $n=1$, we can write $371=7\cdot 53$, and therefore $P(1)$ is true. Let $P(k)$ be true for $k&gt;1$. Then we now have to prove that $P(k+1)$ is true.  I found that $37\underbrace{111\cdots 1}_{k\text{ ones}}$ can be written as $37\cdot 10^k+10^{k-1}+10^{k-2}+\cdots +10^0$ and that $37\underbrace{1111\cdots 1}_{k+1\text{ ones}}$ can be written as $37\cdot 10^{k+1}+10^{k}+10^{k-1}+\cdots+10^0$.  I think I'm pretty close to the answer know, but I don't know how to proceed. I'm very new to Ubuntu, and have come to this point that I can't boot back to my Windows Vista anymore.  I thought that I would get some kind of dual boot in the beginning when booting my computer, but this doesn't seem too happen and I don't have the slightest idea on how to fix this. I was looking for help here at askubuntu, but I couldn't seem to find anything. I'm too new with this software.  I'll need hints and tips on how to fix this  Thanks for your time folks! When the automorphism group is trivial...... If $G$ is a trivial group , obviously $Aut(G)$  is  trivial . Does the converse  hold $?$ .  When  we  are  given  that a  group $G$  has  trivial  automorphism  group , can we  conclude  that the group  will  be  trivial $?$ .  I  guess  not . For  one  thing , we know  that  $$G/Z(G)\cong Inn(G)$$. So , $Aut(G)$ being  trivial  would  imply  that $$G\cong Z(G)$$  i.e.  $G$  is  commutative . But I  see  nothing about $G'$s being trivial .   The problem  is  that  while I cannot  prove  it , I  could  not  find  a  counter example  either , from  among  the  groups  I  am  familiar  with .   What  is  the non-trivial  commutative  group  that  has  trivial  automorphism  group  $?$ C# - how can I get owner's name for a Mutex I have a shared mutex between 2 applications. I want to create an administration console that shows the current owner's name of the mutex.  How can I get the application name that currently owns the Mutex? I'm having a difficult time understanding this statement. Can someone please explain with a concrete example? django manytomanyfield .add() method How do I copy a file in Python?  I couldn't find anything under . I'm trying to re-learn my undergrad math, and I'm using Stephen Abbot's Understanding Analysis. In section 2.7, he has the following exercise:  Exercise 2.7.5 (a) Show that if $\sum{a_n}$ converges absolutely, then $\sum{a_n^2}$ also converges absolutely. Does this proposition hold without absolute convergence?  I'm posting about this here because my answer to that last question about whether the proposition holds without absolute convergence is "Yes", but my suspicions are raised by him merely asking the question. Usually questions like this are asked to point out that certain conditions are necessary in the statement of propositions, theorems, etc. I just want to see if I'm missing something here.  Anyway, here's how I prove the absolute convergence of $\sum{a_n^2}$, and note that I never use the fact that $\sum{a_n}$ is absolutely convergent:  Proof: Let $s_n = \sum_{i=1}^n{a_n^2}$. I want to show that $(s_n)$ is a Cauchy sequence. So, let $\epsilon &gt; 0$ and $n &gt; m$, and consider, \begin{equation}   \begin{aligned}     |s_n - s_m| &amp;= |(a_1^2 + a_2^2 + \cdots a_n^2) - (a_1^2 + a_2^2 + \cdots a_m^2)|\\                 &amp;= |(a_{m+1})^2 + (a_{m+2})^2 + \cdots + a_n^2|\\                 &amp;= |a_{m+1}|^2 + |a_{m+2}|^2 + \cdots + |a_n|^2\\   \end{aligned} \end{equation} Now, since $\sum{a_m}$ converges, the sequence $(a_m)$ has limit 0. Therefore I can choose an $N$ such that $|a_m| &lt; \sqrt{\epsilon/n}$ for all $m &gt; N$. So for all $n &gt; m&gt; N$,  we have, \begin{equation}   \begin{aligned}     |s_n - s_m| &amp;= |a_{m+1}|^2 + |a_{m+2}|^2 + \cdots + |a_n|^2\\                 &amp;&lt; \left(\sqrt{\frac{\epsilon}{n}}\right)^2 + \left(\sqrt{\frac{\epsilon}{n}}\right)^2 + \cdots + \left(\sqrt{\frac{\epsilon}{n}}\right)^2\\                 &amp;&lt; \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2 + \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2 + \cdots + \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2\\                 &amp;= \epsilon   \end{aligned} \end{equation} Therefore $(s_n)$ is Cauchy and $\sum{a_n^2}$ converges. And since $\sum{a_n^2} = \sum{|a_n^2|}$, the series $\sum{a_n^2}$ is absolutely convergent. &#x220E;  Am I doing something wrong here? Am I right in thinking that $\sum{a_n}$ need not be absolutely convergent for $\sum{a_n^2}$ to be absolutely convergent? Matching Gmail filters on BCC mail Integrating Knowledge into an existing website Which browsers are officially supported, and what else do I need? How do I remove the Me-User-Indicator from the Panel? How do I remove the Me-User-Indicator from the Panel?  The indicator contains two items: the written user name and the icon of a human. an analytic function from unit disk to unit disk with two fixed point prove that if  $f:\mathbb{D}\rightarrow\mathbb{D}$ is analytic with two distinct fixed point then $f$ is identity. I thought if one of the fixed points was zero by schwarz lemma this statement is easily proved. but what can I do if fixed points were nonzero? Mac OS X Darwin: how to reset admin password? NSF IIS status date changed, status still pending What mode does the terminal go into when I type a single quote? Homemade coconut milk separates into different layers after a day in the fridge I made some coconut milk. After a day in the fridge there was two layers of liquid in the jar, coconut water and solid coconut which I found out afterwards that it is called coconut butter! When I stir them together to  have my coconut milk back, it didn't work. Is there a way to prevent this? If not, is there a way to have coconut milk again? What is a simple example of a limit in the real world? This morning, I read Wikipedia's informal definition of a limit:     Informally, a function f assigns an output $f(x)$ to every input $x$. The   function has a limit $L$ at an input $p$ if $f(x)$ is "close" to $L$ whenever   $x$ is "close" to $p$. In other words, $f(x)$ becomes closer and closer to $L$   as $x$ moves closer and closer to $p$.   To me that sounds like something that might be better described as a 'target'.  If I take a simple function, say one that only multiplies the input by $2$; and if my limit is $10$ at an input $5$: then I've described something that seems to match the elements contained in Wikipedia's definition. I don't believe that that's right. To me it looks like an elementary-algebra problem ($2p = 10$). To make it more calculusy, I could graph the function's output when I use inputs other than $p$, but that really wouldn't give me anything but an illustration of the fact that one's answer moves farther from the right answer as it becomes more wrong (go figure).   So limits are important; what I've just described is trivial. I do not understand them. I know calculus is often used for solving real-world challenges, and that limits are an important element of calculus, so I assume there must be some simple real-world examples of what it is that limits describe.   What is a simple example of a limit in the real world?  Thank you  -Hal. Suppose that $(s_n)$ converges to s. Prove that $(s_n^2)$ converges to $s^2$ I am really struggling with my proofs class, I don't really understand how to prove a statement like this, or what the epsilon is standing for..  Suppose that $(s_n)$ converges to s.  Prove that $(s_n^2)$ converges to $s^2$ directly without using the fact that $lim(s_nt_n)=st$  Suppose that $(s_n)$ converges to s. Then, since $(s_n)$ is convergent, there exists an $M_1$ such that $|S_n|&lt;M_1$, for all $n\in \!\,\mathbb{N} \!\,$. Let $M=M_1+|S|$ (I don't completely understand this step...). Then given $ε&gt;0$, there exists N such that n>N implies that $|s_n-s|&lt;ε/M$. Thus for n>N, we have $|s_n^2-s^2|=|s_n-s|*|s_n+s|&lt;(ε/M)(M)=ε$. Hence, $s_n^2$ converges to $s^2$.