Calculate $ \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n+1} H_n$
On a series involving harmonic numbers
I have read about copying files with terminal but these examples will help me a lot. So here is what I want to do:  Examples:   I have a file in /home/levan/kdenlive untitelds.mpg and I want to copy this file to /media/sda3/SkyDrive and do not want to delete any thing in SkyDrive directory. I have a file in /media/sda3/SkyDrive untitelds.mpg and I want to copy this file to /home/levan/kdenlive  and do not want to delete any thing in kdenlive directory  I want to copy a folder from home directory to sda3 and do not want to delete any thing on sda3 directory and opposite I want to cut a folder/file and copy to other place without deleting files in that directory I cut it into. I created a Compute Engine VM (Ubuntu 18.04), and when I log into it using the SSH button in the VM instances list I'm logged in as user username.  After a while, I realised I needed to be able to use another SSH client as well. As per  I enabled OS Login by adding a key-value pair in metadata, where key is enable-oslogin and value is TRUE.  I then tried to add my existing SSH key:  gcloud compute os-login ssh-keys add --key-file path/to/key.pub --ttl 0  which was successful except one major problem: it has added the key for user username_gmail_com and will only allow me to ssh to my VM as that user:  ssh username_gmail_com@myinstance  And it has also created that user on my VM. From the web interface, I'm logged in to the VM with that new user as well (/home/username_gmail_com). Of course, I can still access the original user's data (/home/username). When I disable OS Login the web interface logs me in as username again and SSH from another client is disabled.   Why is the username different when enabling OS Login? Can I change the username with OS Login enabled?   Edit  There has been an addition to the docs explaining exactly this question. Check here:  and on  all the way at the bottom under "Expected login behaviors". Why was the MCU Super Soldier program considered a failure? In Marvel Cinematic Universe, military tried to create super soldiers like Hulk, but they failed. So, the program was shut down.  Where did they fail? Didn't Blonsky get Wolverine-type super healing capability? Why couldn't it make the military stronger? Other than this, wasn't Abomination a success (despite the fact that it wasn't an original work of the military)? He was defeated by Hulk, but enemy forces don't have a Hulk. When it comes to anger, who cares as long as you are focused on the target? Abomination was indeed in full control and he was always after Hulk. What does "more buyers than sellers" in technical analysis of stocks actually mean? I often hear/read technical analysts looking at volume and price action on a chart and claiming that there are "more buyers than sellers" or vice versa.  Since every trade requires a buyer and a seller, how can volume/price signify more of one than the other?  What does that actually mean?  When I hear that there are "more buyers," I get the impression they actually mean more "professional" or "institutional" buyers, but I could just be imagining that meaning.  But wouldn't this "more buyers" situation actually represent a smaller number of large buyers placing multiple orders? (and those orders would be matched by a larger number of smaller investors on the other side of the trade?)  Maybe I have my assumptions backwards and "more buyers" is what they say when they actually mean "more retail buyers and less institutional buyers"?  Or maybe the expression has nothing to do with number of buyers/sellers at all and is just some arbitrary technical analysis situation?  What situation is it that they're trying to describe?  If the "smart money" traders had placed larger orders, then there would have to be equally large sellers on the other side of that large trade, right?  I know trades often get broken up, but if the trades had been broken up it would be equivalent to "large traders placing multiple orders" scenario described above.  If the trades were not broken up, then there would not be an imbalance in the "number" of "smart" vs. retail buyers/sellers, right?  UPDATE/EDIT: I usually see this stated in reference to technical indicators such as RSI.  I don't typically hear people saying "there are more buyers than sellers" in the situations you guys are describing with more unfilled orders on one side of the (potential) trade (though that would make more sense if that was what they were talking about).  See for example: Platform diving: How deep does one go into the water? I am a platform diver. I am trying to figure out how deep in the water I go depending on which platform I dive from.  The platforms are 1m, 3m, 5m, 7.5m and 10m above the water surface.  By ignoring air resistance (we assume that I do not do any tricks) I can easily compute the energy that my 90 kg body has when it is hitting the water:  E = mgh = 0.5mv^2   My problem is to find the deceleration in water and thus how deep my feet will go into the water before coming to a halt. We can assume that I stand straight and fall straight down and have a height of 190cm.  How do I compute that? Consider the functional equation problem $$ f : \mathbb R \to \mathbb R \text , $$ $$ f \left( a ^ b \right) = f ( a) ^ { f ( b ) } \text , $$ when $ a , b \in \mathbb R $, $ a , b \ge 0 $. So far the only solution I have is the trivial $$ f ( x ) = x \text . $$ Does there exist any other possible solution? Even if the $ f $ doesn't have a closed form in terms of elementary functions, is there some way I could derive a series or an alternative expression for it? I tried to get a little more creative: $$ f ( w ) = f \left( w ^ { \frac 1 w } \right) ^ { f ( w ) } \text , $$ which nests deep into $$ f ( w ) = f \left( w ^ { \frac 1 w } \right) ^ { f \left( w ^ { \frac 1 w } \right) ^ { f \left( w ^ { \frac 1 w } \right) ^ \vdots } } \text , $$ which is equivalent to $$ \ln \big( f ( w ) \big) = \ln \bigg( f \left( w ^ { \frac 1 w } \right) \bigg) f ( w ) \text . $$ I was hoping to generate some sort of series using this. Converse of Schur's Lemma in finite dimensional vector spaces I am trying to prove (or disprove) the converse of Schur's Lemma in finite dimensional vector spaces. I am not sure if it holds in this case, but I have tried to apply the idea that proves it in representation theory (see for example Theorem 4.3  that uses Maschke's theorem or in questions  and ).  The converse of Schur's Lemma in finite dimensional vector spaces is:     Let $V$ be a finite dimensional vector space over the complex numbers. Let $S$ be a set of endomorphisms of $V$ and assume that every endomorphism $A$ of $V$ such that $$AB=BA\text{ for all }B\in S$$ is of the form $\lambda I, \ \lambda\in\mathbb{C}$. Then $V$ is a simple $S$-space.   (*an endomorphism of $V$ is a linear operator from $V$ to $V$  *$V$ is a simple $S$-space if the only $S$-invariant subspaces of $V$ are $V$ itself and the zero subspace)  What I've tried so far:  Assume to the contrary that $V$ is not a simple $S-$space. Then, there exists a subspace $W$ of $V$ such that $W\not =\{0\}$, $W\not= V$ and $W$ is $S$-invariant. Let $W'=V\setminus W$. Then, since $V$ is finite, we can easily prove that $V=W\oplus W'$ (this is my attempt to translate Maschke's theorem in vector spaces). Consequently, for every $v\in V$, there exists unique $w\in W$ and $w'\in W'$, such that $v=w+w'$. Define the projection $P:V\rightarrow V$ by $Pv=w$ for every $v\in V$.   What is left to prove is that $PB=BP$ for all $B\in S$. Then $P$ is clearly not a scalar and thus we have the contradiction we are looking for.  There is a difficulty in showing that $PB=BP$ for all $B\in S$, because $W'$ might be $S$-invariant or not. More precisely:   Let $v\in V=W\oplus W'$ and $v\not =0_V$.  If $v\in W$ then $Bv\in W$ because $W$ is $S$-invariant, therefore: $PBv=Bv$ and $BPv=Bv$.  If $v\in W'$ then $Pv=0$, hence $BPv=B\cdot 0=0$, and  (i) if $Bv\in W'$ then $PBv=0$.  (ii) if $Bv\in W$ then $PBv=Bv$ and this is where the problem occurs.  Any hints, ideas or counterexamples would be very helpful. I know the so-called textbook definition of unit tests and integration tests.  What I am curious about is when it is time to write unit tests... I will write them to cover as many sets of classes as possible.  For example, if I have a Word class, I will write some unit tests for the Word class.  Then, I begin writing my Sentence class, and when it needs to interact with the Word class, I will often write my unit tests such that they test both Sentence and Word... at least in the places where they interact.  Have these tests essentially become integration tests because they now test the integration of these 2 classes, or is it just a unit test that spans 2 classes?  In general, because of this uncertain line, I will rarely actually write integration tests... or is my using the finished product to see if all the pieces work properly the actual integration tests, even though they are manual and rarely repeated beyond the scope of each individual feature?  Am I misunderstanding integration tests, or is there really just very little difference between integration and unit tests? Expected value in an urn problem In an urn there are $n$ red balls and $m$ blue balls. I extract them without replacement. Let $X$=time of first blue. What is $E(X)$?  I found PMF of $X$ and it is, if $k &gt; n+1$  $$P(X=k) =\frac{n(n-1) \dots (n-k+1)m}{(m+n)(m+n-1) \dots (n+m-k+1)}$$  How could I evaluate $E(X)$?  Edit: I'm looking for an explicit form of $E(X)$ Get Record Type Developer Name without SOQL Query Sometimes chicken breast can be thick and I never know how to tell when it's cooked! How can I be certain it is cooked all the way through? StringPattern to remove markers around text I want to use input from a user as a regex pattern for a search over some text.  It works, but how I can handle cases where user puts characters that have meaning in regex? For example, the user wants to search for Word (s): regex engine will take the (s) as a group.  I want it to treat it like a string &quot;(s)&quot; .  I can run replace on user input and replace the ( with \( and the ) with \) but the problem is I will need to do replace for every possible regex symbol. Do you know some better way ? On my Windows 7 system I installed via  from Fonts.com:   The font does not appear in C:\Windows\Fonts. However, it shows up in certain desktop applications, for example  as: Sabon Next Com Display  My intention was to use the font in a LaTeX document test.tex:  \documentclass{article} \usepackage{polyglossia} \setromanfont{Sabon Next Com Display}  \begin{document} Hello World! \end{document}   Unfortunately, xelatex test.tex fails:  […] Couldn't find `Sabon Next Com Displ.cfg' miktex-maketfm: No creation rule for font "Sabon Next Com Display".   !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ! fontspec error: "font-not-found" !  ! The font "Sabon Next Com Display" cannot be found. !  ! See the fontspec documentation for further information. !  ! For immediate help type H &lt;return&gt;. !...............................................    l.4 \setromanfont{Sabon Next Com Display}                                            % Sabon Next Com Display, SabonNex...  ?    Can XeLaTeX even work with fonts installed via SkyFonts? If not, what could be a workaround? How to convert milliseconds into human readable form? Where can I ask an open discussion question? How do I change the GRUB boot order? I have both Windows 7 and Ubuntu installed on a shared machine. Because a lot of the non-developers use Windows, I'd like to change the boot order to make it easier for them.  Currently the boot order looks like the following:   Ubuntu 11.10 kernelgeneric *86 Ubuntu 11.10 kernelgeneric *86 (safe boot)  Memory test Memory test Windows 7 on /dev/sda6   How do I change the default order so that Windows 7 is at the top of the list?   Windows 7 on /dev/sda6 Ubuntu 11.10 kernelgeneric *86 Ubuntu 11.10 kernelgeneric *86 (safe boot)  Memory test Memory test Ampere's circuital law for finite current carrying wire When I was studying about . Then there comes a question in my mind that "whether this law is applicable for finite current carrying wire or not" We hold an L1 visa (Citizens of India) and are planning a cruise to the Bahamas this summer. Are there any Visa requirements to enter Bahamas. How to fix AppArmor `could not open` error when installing php+mysql?