What is the difference between efficiency and efficacy?
Is there any difference in meaning between 'efficacy' and 'efficiency'?
How to obtain the sum of the following series? $\sum_{n=1}^\infty{\frac{n^2}{2^n}}$ It seems that I'm missing something about this.  First of all, the series is convergent: $\lim_{n\rightarrow\infty}\frac{2^{-n-1} (n+1)^2}{2^{-n} n^2}=\frac{1}{2}$ (ratio test)  What I tried to do is to find a limit of a partial sum $\lim_{n\rightarrow\infty}S_n$ as follows: $S_n=\frac{\frac{1}{6} n (n+1) (2 n+1)}{\frac{1-\left(\frac{1}{2}\right)^n}{2 \left(1-\frac{1}{2}\right)}}$. Still, the limit is $\infty$ and I'm clearly doing something wrong. The Ball From A Pass To prove $ \tan(A) + 2 \tan(2A) +4\tan4A + 8 \cot8A =\cot(A) $ I am trying to solve:  $$\int_{-\infty}^{\infty}\frac{x\sin{x}}{x^2 + a^2}dx$$  and show that it equals $\pi e^{-a}$ for all $a &gt; 0$.  I translate it to its complex equivalent:  $$lim_{R \rightarrow \infty} \int_{-R}^{R}\frac{z\sin{z}}{z^2 + a^2}dz = \int_{C}\frac{z\sin{z}}{z^2 + a^2}dz - \int_{\gamma}\frac{z\sin{z}}{z^2 + a^2}dz$$  where C is a half circle with radius R, above the real axis, and $\gamma$ is only the curved (top part) of the half circle.  I've shown that $$\int_{\gamma}\frac{z\sin{z}}{z^2 + a^2}dz$$ tends to 0 as $R \rightarrow \infty$.  So now:  $$lim_{R \rightarrow \infty} \int_{-R}^{R}\frac{z\sin{z}}{z^2 + a^2}dz = \int_{C}\frac{z\sin{z}}{z^2 + a^2}dz$$  By residue theorem,   $$\int_{C}\frac{z\sin{z}}{z^2 + a^2}dz = 2\pi i \cdot res_{ai}f$$  as $ai$ is the pole of $f$ that lies above the real axis.  $$2\pi i \cdot res_{ai}f = 2\pi i \cdot lim_{z \rightarrow ai} (z-ai)\frac{z sin{z}}{z^2 + a^2}$$  By L'Hospital's rule, this is equivalent to:  $$2\pi i \cdot lim_{z \rightarrow ai} (z-ai)\frac{z^2\cos{z} + 2z\sin{z} - zai\cos{z} - ai\sin{z}}{2z} = 2\pi i \cdot \frac{\sin{ai}}{2} = \pi i \sin{ai}$$  But how is $\pi i \sin{ai}$ equivalent to $\pi e^{-a}$? Did I make a mistake? Plotting a Continuous signal Was "book" to "beek" as "foot" is to "feet"? "Foot" is a curious word in English because it is pluralized in an unusual way; the "oo" in the word is changed to "ee".  Did this once use to be a standard way of pluralizing things in English (or a language that contributed to English), which would mean that the plural of "book" was "beek" instead of "books"?  Or, is "feet" just a one-off? SharePoint 2013 Online - Missing Follow Link In reading through the original GCM specification (), the composition of the 128 bit Initialization Vector as a concatenation of a 96b nonce and a 32b unsigned wrapping counter seems arbitrary and forces the scrambling pattern to repeat every 232 16-byte block.  Is the algorithm expected to be secure for significantly longer stream lengths if for example the IV were a 128b nonce XORed with a 64b or 128b counter, or are there known cryptanalysis issues that begin to arise? Where does the damage of relocated dashes land? The end location of a dash or jump can be changed by an ability that pushes () or pulls () you. So for example I try to  on the adc, but a Blitzcrank pulls me, preventing me from landing on my chosen spot.  Will I deal my AoE damage around the adc, where I tried to land, or around the Blitzcrank, where I ended up landing? How to Expand , Resize "extended partition"? How can I expand/resize my extended partition (sda3) with unallocated free space to the left of it? I want this to be able to expand my / partition (sda5). For subspaces, if $N\subseteq M_1\cup\cdots\cup M_k$, then $N\subseteq M_i$ for some $i$? I have a vector space $V$ over a field of characteristic $0$. If $M_1,\dots,M_k$ are proper subspaces of $V$, and $N$ is a subspace of $V$ such that $N\subseteq M_1\cup\cdots\cup M_k$, how can you tell $N\subseteq M_i$ for some $i$?  I was first trying to show it just in the case $N\subseteq M_1\cup M_2$, and hoping to extend it to finitely many $M_i$. If either of the $M_i$ contains the other, the claim follows, so I suppose neither $M_i$ contains the other.   In hopes of a contradiction, I suppose $N\not\subseteq M_1$ and $N\not\subseteq M_2$, Picking $x_1\in N\setminus M_1$ and $x_2\in N\setminus M_2$, I'd have $x_1+x_2\in N\subseteq M_1\cup M_2$. The only thing I could conclude was that actually $x_1,x_2\notin M_1$ and $x_1,x_2\notin M_2$, which seems like a dead end. What's the right way to do this? Determine if Term has Grandparent/Great-Grandparent How to install XAMPP? Hi all im a noob on Ubuntu/Linux World,  So i need some that give a full tutorial to How to install  from apachefriends.org correctly on Ubuntu 11.10 + all beyond Ubuntu for 32 bit and also 64 bit Desktop Version.. and also i need this:   Make a Folder on Your Home Folder and Linked to htdocs from Apache Web Server Make a GUI interface for Xmapp Start Xampp when Ubuntu Boot Up or Start Ubuntu   (Note: i ask it for both X86 and X64 so people in the further can see the tutorials)    New Data:  What i did was i download from  for now and i also what to say that I'm currently running Ubuntu 11.10 X64 bit for Dell Studio 1558 processor intel i3  i will let you know guys which solution was the best, and it is for a Desktop Version of Ubuntu 11.10 (Laptop 15 inch screen ^_^ ) not Server Ubuntu Add a property to a JavaScript object using a variable as the name? I'm pulling items out of the DOM with jQuery and want to set a property on an object using the id of the DOM element.   Example  const obj = {}  jQuery(itemsFromDom).each(function() {   const element = jQuery(this)   const name = element.attr('id')   const value = element.attr('value')    // Here is the problem   obj.name = value })   If itemsFromDom includes an element with an id of "myId", I want obj to have a property named "myId". The above gives me name.  How do I name a property of an object using a variable using JavaScript? There's vs There are For example:     There's two options here   or     There are two options here   I hear a lot of people say the first line (or something similar), but isn't that incorrect? Isn't it plural and therefore you should use "there are"? How do I find a command if I don't know its name? I am running Ubuntu 14.04 on think-pad T450.  When using an external monitor with higher resolution than the in-built laptop screen, the text of dialog boxes are getting messed up.  Looks like I need to replace the Graphic card driver. Anyone found a solution to this?  Updated to add requested information:  lspci -nnk | grep '\[03' -A2   gives the following:  00:02.0 VGA compatible controller [0300]: Intel Corporation Broadwell-U Integrated Graphics [8086:1616] (rev 09)     Subsystem: Lenovo Device [17aa:5034] Kernel driver in use: i915   Below is a screenshot, see how the letters are messed up on the screen. What is the difference between “do” and “make”? Is it possible to redirect a command's output to cd? For example, I searched for a directory using locate and got the path to it. Now, instead of writing a cd path, can I redirect the locate output to cd?  I tried this:  $ locate Descargas | grep Descargas$ /home/oliver/Descargas $ locate Descargas | grep Descargas$ | cd $ locate Descargas | grep Descargas$ &gt; cd $ locate Descargas | grep Descargas$ &lt; cd /home/oliver/Descargas $    No luck. This probably isn't particularly useful, but I'm curious. Invalid Data Source when importing geojson to QGIS Im trying to import geojson, I add data, select protocol and use the uri  QGIS says "Invalid Data Source:  is not a valid or recognized data source"  I've followed the tutorial here  but I cant get the data to come in, any ideas? I'm using QGIS version 2.18.13