How to calculate the nth term of sequence that increases by n?
Formula for the $n$th term of $1, 2, 2, 3, 3, 3, 4, 4 ,4, 4, 5, ...$
I want to reinstall Ubuntu, but I also want all information and settings to disappear. So everything looks like the first time I installed it. Is it possible to do so via Terminal? Or what are the steps I should follow? Let $p$ a cut point of a connected space $(X, \mathcal{T})$ and suppose $C$ and $D$ form a separation  of $X-\{p\}$, i.e $$X-\{p\}=C \cup D$$ Prove that $C \cup \{p\}$ is conected. I have this idea: Since $p$ is a cut point then $X-\{ p \}$ is not connected, and since $C$ and $D$ form a separation of $X- \{p \}$ then $X-\{p \} = C \cup D$, and also $C \cup D$ is not connected. And also $$C \cap \overline{D}= \overline{C} \cap D= \emptyset$$ I need an idea to continue please How do I delete an entity from the Minecraft world folder? How can I send an email using a template? I have created a email template in ExactTarget API and I want to use it executing XML from SoapUI.  Is there any tutorial or examples of how can this be done?  I'm new at this and I'm not sure how ExactTarget really works. What formats supporting animation are suitable for the web? What formats supporting animation are suitable for the web and what are the pros and cons of each. Proof of lack of pure prime producing polynomials. I recently encountered this following proposition:  For every polynomial, there is some positive integer for which it is composite.  What is the most elementary proof of this? Floor a date in SQL server In SQL Server, how do I "floor" a DATETIME to the second/minute/hour/day/year?  Let's say that I have a date of 2008-09-17 12:56:53.430, then the output of flooring should be:   Year:  2008-01-01 00:00:00.000 Month: 2008-09-01 00:00:00.000 Day: 2008-09-17 00:00:00.000 Hour: 2008-09-17 12:00:00.000 Minute: 2008-09-17 12:56:00.000 Second: 2008-09-17 12:56:53.000 Automatically Locate Included Images Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule] I am working on a problem I am pretty close to solving but I can't figure out the last part. I used some algebraic manipluation to break the problem down. The problem is:     Show that the following congruence is true      a^b = ((a mod n)^b) (mod n)      for any positive integers a, b, and n.      Hint: Number a can be written as a = q*n + r, where q = floor brackets a/n, and r = a mod n.   My attempt it:     (q*n +r)^b = ((a mod n)^b) * (mod n)      (q*n)^b + (a mod n)^b = ((a mod n) ^b) * (mod n)      (a)^b -(r)^b = ((a mod n) ^b) * (mod n)      (a)^b = modn  ----> divided by ((a mod n)^b)   Am I doing this correctly and if so how can I prove this is true? Is there a trick I am missing? I think that by simplifying it further I would just keep going in a loop.  Thanks! Are +1/+1 counters different from +1/+1 effects? How to use PostgreSQL/PostGIS with ArcGIS for Desktop? I recently read that:     What our current level of thermodynamics does tell us though is that if there is such a thing as a Big Crunch, the universe will look a lot different as it heads towards collapse than it did when expanding – the universe started in a state of low entropy and high order and will end in a state of high entropy and   low order.   But shouldn't the order be in a high state and hence entropy becomes a low state in the Big Crunch (assuming a closed universe)?  The reason I write this is because the gravitational forces in a closed universe are so strong they will cause gravitational collapse so the universe will shrink and go backwards, eventually through all the stages of the big bang and become a singularity once more.   It was my understanding that a singularity has a state of high order and low entropy. Have I got this the wrong way round?   If so; Can someone please explain why? What is the use of anonymous classes in Java? Can we say that usage of anonymous class is one of the advantages of Java? Windows 8 removes Grub as default boot manager I have a Sony VAIO S series with Windows 8 preinstalled, and I installed Ubuntu 12.10 on a new partition. When the PC boots Grub is display, and I can choose between Windows 8 (didn't worked at the beginning, had to change Grub settings) and Ubuntu 12.10. When I select Ubuntu 12.10 everything is OK, but when I use Windows 8, and I restart Grub isn't displayed anymore (Windows 8 boots immediately).  I booted a Ubuntu 12.10 LiveUSB, used efibootmgr, and found out that Windows 8 (each time it boots) changes EFI default bootloader from Grub to Windows Boot Manager.  How do I change this in Windows 8? I read something about bcdedit, but it does not work or I don't know how to use it... Suppose I wanted to travel to one of the recently discovered potentially Earth-like planets such as Kepler 186f that is 490 light years away. Assuming I had a powerful rocket and enough fuel, how long would it take me? Does separation of variables in PDEs give a general solution? When a partial differential equation is solved using the separation of variables method, is the produced solution the most general one that satisfies the equation or have we lost some forms of the solution because of the assumption that it is in the form of separated variables? When I start a sentence with words like "someone" or "somebody", I don't know how to choose the right pronoun at the end of the sentence.  Examples:      If anybody asks you about the money, tell (Him - Her - It - Them) that it is in my bank account.     I felt that somebody was in the garden but I did not see (Him - Her - It - Them).     Speaker 1: A friend of mine helped me a lot.      Speaker 2: You should thank (Him - Her - It - Them).     Congratulations on your new baby! What's (His - Her - Its - Their) name?    Those are the cases or situations that I can think of. If you have any other different situations, please let me know. Spambots causing server crashes. How do I block them? I was confused initially about what the pins mean next to a topic in the new help center.  "those articles are "featured" articles; they are meant to draw attention to the most important site policies or most frequently encountered issues."   If the pin is used to denote an important topic, it should at least be noted as such. Also a pin generally means to me that this is something that I personally selected.  Could their meaning be clarified somehow? I have a problem with derivation of some function. This is related to computing the Poincare Map of Logistic Population model with Periodic harvesting. This function is:  $\phi(t,x_0) = x_0 + \int_{0}^{t} f(s,\phi(s,x_0)) ds $,  where $\phi(t,x_0)$ is a function: $\mathbb{R}  \times \mathbb{R} \rightarrow \mathbb{R}$.  I'm trying to differentiate  equation of this function both sides  with respect to $x_{0}$. In book from this equation comes from the result of this differentiation is:  $\frac{\partial \phi}{\partial x_0} (t,x_0) = 1 + \int_0^{t} \frac{\partial f}{\partial x_0} (s, \phi(s,x_0)) \cdot \frac{\partial \phi}{\partial x_0} (s, x_0)ds$.  I can't understand expression under the integral. In this book it is explained that it is clear from chain rule.Could someone explain to me this transformation in easy way? I will be grateful for your help Best regards