What is $\lim_{x\to \infty} 2\sqrt{x}- \sum_{n=1}^x {1\over \sqrt{n}}$?
Evaluate: $\lim_{n\to\infty}\left({2\sqrt n}-\sum_{k=1}^n\frac1{\sqrt k}\right)$
I have a MicroSD card in a USB adapter (which plugs into a USB port on my machine, and acts like a USB flash drive). I was using Unetbootin to make this a bootable USB flash drive with Kubuntu. But I needed to cancel while it was working. So I killed the Unetbootin process from the console.  Since then, I can't format the MicroSD or delete the folder that Kubuntu made. I have also tried mkdosfs, with no success. I can't mount the drive anymore either? What can I do to make this drive usable again?  Trying to create a new partition table in GParted, as described in Eliah Kagan's answer, does not work. It fails with the error message "imposible crear tabla de particiones" ("unable to create a partition table"). Today I started having the following issues in Pokémon GO:   I can't spin pokéStops and get rewards When I catch pokémon, even the lowest CP ones, they escape every time. I've tried using razz berries, that doesn't work. Neither does using great balls.   I do have Internet. I'm not on wifi. I can send messages and browse Internet.  NOTE: I did try to modify my gps location and I was unsuccessful. I only got a pokémon or two and deleted them immediately. I do apologize for trying to hack it but I'm now fully legit. Is there an GUI Designer for python? Is there a GUI IDE for programming python just like java has netbeans?  I wanted one where we could drag &amp; drop test boxes &amp; labels just as we do in swing components using netbeans or eclipse.  Or is there an add-on present in either netbeans or eclipse itself? Why can't I chown a VirtualBox shared folder? Why do wheels appear to revolve opposite to the direction they are rotating? When viewing cars that are driving along side of us, sometimes their wheels appear to be turning backwards even though they are traveling in the same direction as our car. Why do they look that way? Show the number of up-votes and down-votes on the mobile site theme Browser back leaves page after going fullscreen in stack snippet Opening a Stack Snippet in full screen should use history.pushState() to add an entry to the browser history stack. Clicking back will then close the snippet rather than leave the page completely. Let $f \in C [a,b]$ such that $\forall x\exists y$ such that $|f(y)| \leq \frac{1}{2}|f(x)|$. Prove that $\exists c\in [a,b]$ such that $f(c) = 0$. Why does Javascript getYear() return 108? Construct a fourth circle tangent to 3 circles forming a tangency chain $G$ a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$ Let $G$ be a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$  I know G is abelian since $ab = (ab)^{-1} = b^{-1} a^{-1} = ba$ for all non-trivial $a,b \in G$ so I have several questions remaining:    How do I prove $|G| = 2^n$? I'd like to say we use induction to prove this but I'm at a loss as to where I would start. Why is $G \simeq C_2 \times C_2 \times\cdots\times C_2$?   I've read several answers to question similar to this yet unfortunately most of them involve Galois Fields and vector spaces, both concepts I'm unfamiliar with. I'd greatly appreciate an intuitive proof. "On their back" or "on their backs"? After the therapy, eight children (43%) became able to crawl/move on their back.   Or should I use "on their backs"?   Singular because each child only has one back, or plural because we're dealing with eight backs? I'd like to ask for help with a task that I've been given.  The task goes like this: In a poker game (52 cards), 5 players are given 5 cards each. What is the probability that both the first and the third player will get a full-house?  It's apparent that the probability of the first player getting a full house is  $\frac{\binom{13}{1} * \binom{4}{3} * \binom{12}{1} * \binom{4}{2}}{\binom{52}{5}}$  Then the second player gets 5 random cards, so $\frac{\binom{13}{1} * \binom{4}{3} * \binom{12}{1} * \binom{4}{2}}{\binom{52}{5}} * \binom{47}{5}$  Now the third player is supposed to get a full house, I'm assuming it should look like this: $\frac{\binom{13}{1} * \binom{4}{3} * \binom{12}{1} * \binom{4}{2}}{\binom{52}{5}} * \binom{47}{5} * \frac{\binom{13}{1} * \binom{4}{3} * \binom{12}{1} * \binom{4}{2}}{\binom{42}{5}}$  The fourth and the fifth player both receive 5 random cards, so the final equation should be:$\frac{\binom{13}{1} * \binom{4}{3} * \binom{12}{1} * \binom{4}{2}}{\binom{52}{5}} * \binom{47}{5} * \frac{\binom{13}{1} * \binom{4}{3} * \binom{12}{1} * \binom{4}{2}}{\binom{42}{5}} * \binom{37}{5}* \binom{32}{5}$  This is how I would solve the task, but I'm not sure that my solution for the third player is correct. Could anyone more experienced than me have a look at my solution?  Also I'm sorry if there is a solution for this type of task on this site, I tried looking for it and I found a lot of poker probability questions, most of them were however focused on only one player and not multiple players, which is my case. Solve $x^2+5x+6 \equiv 187 \mod 187$ Solution $$x^2+5x+6 \equiv 187 \mod 187$$ $$ (x+\frac{5}{2})^2 \equiv \frac{1}{4}$$ $$ 4(x+\frac{5}{2})^2 \equiv 1$$ $$ y:= x+\frac{5}{2} $$ $$ 4y^2 \equiv 1 \mod 11 \wedge 4y^2 \equiv 1 \mod 17  $$ $$ ( 2y \equiv 1 \mod 11 \vee 2y \equiv 10 \mod 11 ) \wedge ( 2y \equiv 1 \mod 17  \vee 2y \equiv 13 \mod 17)  $$ $$ ( y \equiv 6 \mod 11 \vee y \equiv 5 \mod 11 ) \wedge ( y \equiv 9 \mod 17  \vee y \equiv 15 \mod 17)  $$ Combining that from CRT I got: $$ y \in \left\{49, 60,83,94 \right\} $$ and for example: $$ x+\frac{5}{2}  \equiv 94 \mod 187$$ $$ 2x  \equiv 183 \mod 187$$ some calculus and get... $$x \equiv 185 $$ And the same thing for each other case. Question Is there any faster (or smarter) way to solve equations like that? Checking for valid floating point number How can I generate isometric sprite sheets from 3D animations? I have a DVD I was trying to rip, and handbrake froze up when scanning it.  I tried to eject the DVD by dragging and dropping it to the trash, which trashed the icon, but didn't eject the DVD.  I then forced Handbrake to quit, but without an icon on my desktop to select, how can I eject the DVD? While I was reading the book Exploratory examples for real analysis, I came across this:     to show that : $$\lim_{x\rightarrow x_o}\frac{1}{h(x)} = \frac{1}{\lim_{x\rightarrow x_o}{h(x)}} = \frac{1}{M}$$      Discussion:Let $\epsilon \gt 0$.we want to find $\delta \gt 0$ such that       if  $0 \lt |x-x_0| \lt \delta $,then $\Big|\frac{1}{h(x)}-\frac{1}{M}\Big|\lt \epsilon$.      In order to get expression involving $|h(x)-M|$,we first find the common denominator:        $\Big|\frac{1}{h(x)}-\frac{1}{M}\Big|=\Big|\frac{M-h(x)}{M~h(x)}\Big|$      $~=\Big|\frac{h(x)-M}{|M|~|h(x)|}\Big|$.      As we have to deal with variable term $|h(x)|$ in denominator.We can construct bound .Let $\epsilon =\frac{|M|}{2}$ ,since lim$_{x\to x_o}h(x)=M$,there exists $\delta_1\gt 0~~$ s.t.       if $0 \lt |x-x_0| \lt \delta_1 $,then $|h(x)-{M}|\lt \frac{|M|}{2}$.      As you study steps below,identify that step where $h(x)\neq 0$ for all $0 \lt |x-x_0| \lt \delta_1 $ plays a critical role:      $|M|=|M-h(x)+h(x)|$      $~~~~~~\leq |M-h(x)|+|h(x)|$      $~~~~~~= |h(x)-M|+|h(x)|$      $~~~~~~\lt \frac{M}{2}+|h(x)| \implies$      $\frac{|M|}{2} \lt |h(x)| \implies$      $\frac{1}{h(x)}\lt \frac{2}{|M|}$,where $0 \lt |x-x_0| \lt \delta_1 $.      Now that we've bound for $1/h(x)$,we can apply the definition to term $|h(x)-M|$.      Since     lim$_{x\rightarrow x_o}h(x)=M$,we can find $\delta_2 \gt 0$ such that,       $~~~~~~~~~~~~~~~~~~~~~~~~~~~~$if  $0 \lt |x-x_0| \lt \delta_2$, then $|h(x)-M|\lt \frac{|M|^2 \epsilon }{2}$   The thing I can't understand is for what purpose did the author work with such complicated expression involving $\epsilon $ in the end of the discussion? Calculate sum of series $\sum \frac{n^2}{n!}$ I have to calculate sum of series $\sum \frac{n^2}{n!}$. I know that $\sum \frac{1}{n!}=e$ but I dont know how can I use that fact here.. What bends fabric of space-time? I know that mass can bend fabric of space-time, which causes gravity by making an object curve around a planet or star but is there anything else that can bend it?  Other energy sources, forces anything?