Solving homogenous recurrence relation
Solving recurrence relation. Recurrence
Linear congruence fill in the missing step? Currently working on this problem and I'm having trouble seeing how it goes from one line to the next.    $45x \equiv 63\mod 11$ goes to $x \equiv 8\mod 11$     Any help would be awesome thanks.  Please try to explain how it works to help me see thanks. Prove that a set of connectives is inadequate Refreshing SFDC page from VF frame: CORS issue Show that if $f(z)=\sum\limits_{n\geq0}a_nz^n$ is analytic in $\{z\in\mathbb{C}:|z|&lt;1\}\cup\{1\}$ and $\forall n\geq0:a_n\geq0$ then the radius of convergence of the power series is strictly larger than $1$.  My approach:   Let $D=\{z\in\mathbb{C}:|z|\leq1\}$.  We have that $f(1)$ converges, so $\sum\limits_{n\geq 0} a_n&lt;\infty$. Moreover since the $a_n$'s are all positive we have that $|a_n|=a_n$, therefore $\sum\limits_{n\geq 0} |a_n|=\sum\limits_{n\geq 0} a_n&lt;\infty$.  Let $f_n(z)=a_nz^n$, then $\forall z\in D, n\geq 0$ we have:  $$|f_n(z)|=|a_nz^n|=|a_n|\cdot|z^n|=a_n\cdot |z|^n\leq a_n\cdot 1^n\leq a_n$$  Then, applying Weierstrass M-test we get that the power series is convergent in $D$.  Now, I need to "find" an open ball $B$ such that $D\subset B$ and the power series is convergent in it.  Edit  $f$ is analytic in $1$, so there is an open set $U$ that contains $1$ such that   $$f(z)=\sum\limits_{n\geq 0} b_n(z-1)^n$$  Does it mean that the series is convergent in $U$?   I can see that we have that the two series coincide in $D\cap U$. Can a black hole be explained by Newtonian gravity? In the simple explanation that a black hole appears when a big star collapses under missing internal pressure and huge gravity, I can't see  any need to invoke relativity. Is this correct? Poll on best VNC / remote desktop software for assisting others on Windows/Mac machines from Ubuntu?    I've heard good things about TeamViewer and Fog Creek Copilot, but I'm wondering if the included GNOME Vinaigre VNC client is good enough for this.  To specify, I'm looking for best option based on:   SIMPLEST ease-of-use for client to download/use on their end. See #1. Works cross-platform I am able to control client's mouse and/or keyboard from remote machine. can I reflectively instantiate a generic type in java? Is it possible to reflectively instantiate a generic type in Java? Using the technique described  I get an error because class tokens cannot be generic. Take the example below. I want to instantiate some subclass of Creator that implements Creator. The actual class name is passed in as a command line argument. The idea is to be able to specify an implementation of Creator at runtime. Is there another way to accomplish what I'm trying to do here?  public interface Creator&lt;T&gt; {     T create(); } public class StringCreator implements Creator&lt;String&gt; {     public String create() { return new String(); } } public class FancyStringCreator implements Creator&lt;String&gt; {     public String create() { return new StringBuffer().toString(); } } public static void main(String[] args) throws Exception {     Class&lt;?&gt; someClass = Class.forName(args[0]);     /*ERROR*/Class&lt;? extends Creator&lt;String&gt;&gt; creatorClass = someClass.asSubclass(Creator.class);     Constructor&lt;? extends Creator&lt;String&gt;&gt; creatorCtor = creatorClass.getConstructor((Class&lt;?&gt;[]) null);     Creator&lt;String&gt; creator = creatorCtor.newInstance((Object[]) null); }   Edit: I like Marcus' approach as being the most simple and pragmatic without circumventing the whole generics thing. I can use it in my situation because I can specify that the class passed must be a subclass of StringCreator. But as Ericson pointed out the generic information is still there at the type level, just not at the runtime level so it is still possible to reflectively examine whether a given class implements the correct generic type. I have 2 HDD drives in my computer. At the moment second drive is mounted as /media/storage.  How can I move my user data from /home to /media/storage/home?  Can I just move the data over there and then simply symlink it back? iMac only show flashing folder with question mark after formatting OS X partition drive Today i format my "OS X El capitan" partition for installing "Yosemite". But due an error in bootable yosemite usb it didn't install on this partition. After some hours when i turned on iMac and hold down "option" key for boot into usb but just blank screen and mouse show. And every time when i turend on iMac it only show flashing folder with question mark. I've tried to resolve it by reseting "NVRAM". But after restarting problem still same.  Also I've tried many "Startup key combinations for Mac" but didn't work any combination on startup.  Also i have important data in my other one partition. Please can anyone tell me what i do for resolving that issue Without loosing my data? Firefox application associations not working in the 'Downloads' window I'm trying to set an alias for sudo !! in Bash. I tried alias sbb='sudo !!', but it interprets that as a literal  !! and prints   sudo: !!: command not found   If I use double quotes, it substitutes the double bang in the string itself, so that doesn't work.  Is there any way to make this work? Or an alternative alias? ` Arabic Stack Exchange? I have been learning some Arabic mostly for fun. I am looking for the Arabic Stack Exchange site but cannot find it. I am sure I saw it lying around a few months ago or so. Any idea what happened to it? How should I handle taxes for Minecraft server donations? I run a Minecraft server and there is a donation button so players can help support the costs. I pay out of pocket for the rest, it's $125/mo.  The money they donate goes right to paypal which is where the automatic payment to the server happens, so it works out nice as it will just pull the remaining amount from my account.  Do I need to claim the donations as income? Can I somehow write off the server costs? Etc. I opened the PC in the morning, and this is what I got:      As is visible the icons of the UWA apps were no affected and the start menu also is unaffected.    When Control Panel is in category view the entire page is empty and in large/small icons the name is visible, no icons.  I deleted the iconcache.db in %USERPROFILE%\AppData\Local folder. Following the instructions here: . But to no avail and now windows is not rebuilding the cache.   I also ran sfc /scannow but no changes took place.  What should I do?  (01/01/2016 8:00PM GMT +5:30) Edit: I tried opening the system properties and I got 0x8000ffff error and this:        Then I closed the popup and pressed the OK button on the System Properties Windows and I got 0x8007057A error:      Opening the Image Backup Control Panel page I again got an 0x8007000E error:        I tried using system restore via advanced startup but once again I got 0x800FFFF error.  P.S.: I did try restarting, didn't work. Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$ Let $A,B$ be matrices $m\times n$ $(A, B \in M_{m\times n}(R))$. How can we prove that $$\operatorname{rank}(A+ B) \le \operatorname{rank}(A) + \operatorname{rank}(B)\ ?$$ Probability of two uniform random numbers being more than $\frac{1}{2}$ apart Two numbers are chosen randomly and independently from the unit interval $(0,1)$.  What is the probability that they differ by more than $\frac{1}{2}$? Hint: Think of the $2$ numbers chosen as coordinates in the Cartesian plane. Draw a square with vertices at $(0,0)$,$(1,0)$,$(1,1)$, and $(0,1)$. Allowable choices for the $2$ points lie below the line $y=x-\frac{1}{2}$ or the above $y=x+\frac{1}{2}$. Find the combined area of these regions.  I need help on this. I know what $y=x-\frac{1}{2}$ and $y=x+\frac{1}{2}$ looks like but I am not understanding the problem as a whole Why does Stack Exchange ask for a reload on successful automatic login? I'm looking for an answer considering both technical limitations and user experience.   Does it need a reload from a technical standpoint? A does the same B as does C How can I work with file uploads during a Webdriver test? This is a canonical question, intended to provide a comprehensive answer to many related questions  During the course of a Webdriver test, I want to upload files. However, this opens a native file picker, which Webdriver doesn't seem to support interacting with. How do I interact with it? Conditional Expectaction 3 variables Suppose $X,Y$ and $Z$ are multivariate normal with means and full covariance matrix. The conditional expectation $E(X | Y)$ is well know. What is the conditional expectation of $E(X | Y,Z)$ if $Y$ and $Z$ (and $X$) are correlated? Standard textbooks only seem to cover the case when $Y$ and $Z$ are uncorrelated.