Finding the value of the infinite sum $1 -\frac{1}{4} + \frac{1}{7} - \frac{1}{10} + \frac{1}{13} - \frac{1}{16} + \frac{1}{19} + ... $
Prove that $\sum_{n=0}^\infty \frac{(-1)^n}{3n+1} = \frac{\pi}{3\sqrt{3}}+\frac{\log 2}{3}$
So I've been pulling my hair out over this for the last couple days now, I can't seem to find any solutions that work. I've fresh installed Ubuntu Gnome 16.04 on my system which has no other OS's running on it. Everything's fine aside from the fact that the default Nouveau display driver seems to be causing the UI to freeze sporadically every now and then. No problem right? Just install the proprietary drivers for my GPU and we should be golden? Well here's the thing, no matter how I try to get my GPU's drivers installed I always seem to hit some sort of issue. Here's what I've tried so far:   Switch to the proprietary driver from within the 'Software &amp; Updates' app in Ubuntu. For me the only option available is the 'NVIDIA binary driver - version 375.66 from nvidia-375 (proprietary, tested)'.    After selecting this driver it goes through the install process, asks me to 'configure secure boot' by entering a password, etc. This all seems to work fine initially until I reboot, but then before I see the login screen it seems to open a virtual terminal (usually accessed via alt+shift+F1), but then immediately boots me back to a black screen where it will flash this terminal for a split second every 4 seconds or so. I can access this terminal by using alt+shift+F1, and go on to use it as normal, but it will continually boot me back out to the black screen every few seconds. The only way I can solve this is to keep accessing the terminal each time it boots me out while I purge the nvidia drivers using sudo apt purge nvidia-*. After purging I'm then able to access the login screen and access my Ubuntu again as normal, besides having to reboot to presumably activate the Nouveau drivers again otherwise the resolution is all messed up and only one of my three monitors has anything displayed on it.    Using the steps listed  I download the latest stable/certified driver for my GPU (which as of writing this is version 384.69). However on step 3 where it instructs me to run the driver using sudo sh, I reach an issue where the installer informs me that I need to disable the Nouveau driver in order to continue. I've tried everything from uninstalling Nouveau using 'sudo apt-get remove --purge xserver-xorg-video-nouveau` to blacklisting Nouveau using the steps listed , by editing the 'nvidia-graphics-drivers.conf'.    Unfortunately no matter what I do to try and disable Nouveau the installer always informs me that the Nouveau driver is enabled and needs to be disabled in order to continue. What's funny is that I managed to install the driver using this method once before, but for the life of me I can't get it to work again.    Finally, I've attempted to install the driver by installing the PPA. I run sudo add-apt-repository ppa:graphics-drivers/ppa, sudo apt update, and finally going back into the 'Software &amp; Updates' app and select the 384.69 driver. However after going through the install process the same issue as described in my first method (1.) occurs.    I've also tried switching between gdm3 and lightdm with all 3 methods to no avail. I'm at a complete loss as to what to do. If anyone has any possible solutions I'd love to hear them, because right now I'm at the end of my tether.   If you require any further information just let me know and I'll be more than happy to provide it.   System info:   AMD FX-8350  Nvidia GeForce GT710 1gb  16gb RAM  Ubuntu Gnome 16.04 LTS I am a EE grad. student who has had one undergraduate course in real analysis (which was pretty much the only pure math course that I have ever done). I would like to do a self study of some basic functional analysis so that I can be better prepared to take a graduate course in that material in my university. I plan to do that next fall so I do have some time to work through a book fully. Could some one recommend some good books to start working on this?   Thanks in advance Disclaimer Yes, I am fully aware that what I am asking about is totally stupid and that anyone who would wish to try such a thing in production code should be fired and/or shot.  I'm mainly looking to see if can be done. Now that that's out of the way, is there any way to access private class members in C++ from outside the class?  For example, is there any way to do this with pointer offsets? (Naive and otherwise non-production-ready techniques welcome) Update As noted in the comments, I asked this question because I wanted to write a blog post on over-encapsulation (and how it affects TDD).  I wanted to see if there was a way to say &quot;using private variables isn't a 100% reliable way to enforce encapsulation, even in C++.&quot;  At the end, I decided to focus more on how to solve the problem rather than why it's a problem, so I didn't feature some of the stuff brought up here as prominently as I had planned, but I still left a link. At any rate, if anyone's interested in how it came out, here it is:   (I suggest reading it before you decide that I'm crazy). I have been wondering why anyone ever thought that we could find an expansion for eigenstates of some perturbed Hamiltonian in terms fo those for the basis Hamiltonian. My lecturer insisted that this was because the eigenstates of the Hamiltonian are complete', however from my (limited) understanding of the mathematical basis of QM:   When you are given a Hamiltonian, it comes with the Hilbert space of functions of which it acts (subject to some conditions we impose, such as the Lebesgue square-integrability of functions) When you are given another Hamiltonian, there is no guarantee that it will act on the same Hilbert space Therefore, that the zeroth order Hamiltonian has eigenstates forming a complete basis for the space on which ti acts does not guarantee that these same eignestates form a complete basis for the Hilbert space on which the purturbed Hamiltonian acts.   As a simple example. I can imagine adding a small perturbing magnetic field to a Hamiltonian in which there initially is none, such that we lose the degeneracy in the eigenstates accounting for different spins of a particle. One could say that we have the same Hilbert space before and after but we lose degeneracy; or I would have been tempted to say that our initial Hilbert space did not have these extra dimensions corresponding to the spin states. So rather than the eigenstates of the basis Hamiltonian also forming a complete basis for the purtubed Hamiltonian, but having eigenvalue degeneracy which is lifted on the purtubration, I would have said that our Hilbert space has changed. After all, if we take the former view (i.e. a basis accouting for spin but with degeneracy) then it seems like for any problem we would need to know and account for EVERY possible system property that can be discerned. This doesn't seem reasonable to me....  NOTE:  1) My question was asked here previously:   although there is only a discussion and no conclusive answer given. I see that the distinction is important in relativistic QM, and the case of adding a potential onto a free particle Hamiltonian seems to be a special one. Although I am still not sure what the answer is for general purturbations.  2) Similar question here:   but it seems to completely avoid answering the question. How to proof that $\forall n \ge 1: \sum_{i=1}^n (i(i+1))^{-1} = n(n+1)^{-1}$ using mathematical induction So for a better presentation:   I need to prove this using mathematical induction, so i started with a base of $n=1$  Since $i$ starts at $i = 1$ I got this:  $$\frac{1}{i(i+1)} = \frac{n}{n+1}$$ $$\frac{1}{2} = \frac{1}{2}$$  So since this was true I went to the induction part: I chose $n = k$ and assumed this was true:  $$\frac{1}{i(i+1)} = \frac{n}{n+1}$$ $$\frac{1}{i(i+1)} = \frac{k}{k+1}$$  but I got stuck here since I didn't know if I needed to increment $i$ or not and because I didn't know if I needed to add the summation symbol or not and needed to do a few things with it. Is $f(x,y) = |xy|$ differentiable in $(0,0)$? I have no idea how to approach this problem. How do I find the privileges I have earned and will earn in Stack Overflow? It used to be off the top bar, now its gone  Where has it moved?  EDIT:  It moved onto the profile page !  Right side same row as your name in profile:    Thank you Will airlines compensate me if my entertainment system is not working? In long haul flights, if I get a seat and after take off I found out that entertainment system is not working, I asked a flight attendant to change my seat but she apologized because there are no empty seats to move to.   Is it common to ask for a compensation for such an inconvenience? do major airlines compensate you in such cases? What is the meaning of the axes in t-SNE? I'm currently trying to wrap my head around the  math. Unfortunately, there is still one question I can't answer satisfactorily: What is the actual meaning of the axes in a t-SNE graph? If I were to give a presentation on this topic or include it in any publication: How would I label the axes appropriately?  P.S: I read  Reddit question but the answers given there (such as "it depends on interpretation and domain knowledge"), don't really help me to understand this. Taylor series expansion for $f(x)=\sqrt{x}$ for $a=1$ Freestyle with multiple objects I have several objects that intersect each other:   I would like to draw lines on the silhouette and key details with Freestyle, however Blender does detect intersections between objects and gives a very strange result:   What I'm trying to make is something like this:   Note: This is just an example, what I'm trying to do has about 10 highly detailed objects which intersect each other, so manually combining them is not possible.  Is it possible to make Freestyle detect edges at face intersections? If not, is there a simple way of combining the objects to create a single object with the outer faces of all the objects? Create model from XYZ data points Given the Python function:  def a_method(arg1, arg2):     pass   How can I extract the number and names of the arguments. I.e., given that I have a reference to func, I want the func.[something] to return ("arg1", "arg2").  The usage scenario for this is that I have a decorator, and I wish to use the method arguments in the same order that they appear for the actual function as a key. I.e., how would the decorator look that printed "a,b" when I call a_method("a", "b")? Show Kripke's model proving that the following formula isn't tautology in intuitionistic logic. $ \neg ( p \wedge q ) \implies (\neg p \vee \neg q) $  Please help/hint me ;) Which loss function is correct for logistic regression? I read about two versions of the loss function for logistic regression, which of them is correct and why?  From  (in Chinese), with $\beta = (w, b)\text{ and }\beta^Tx=w^Tx +b$: $$l(\beta) = \sum\limits_{i=1}^{m}\Big(-y_i\beta^Tx_i+\ln(1+e^{\beta^Tx_i})\Big)  \tag 1$$  From my college course, with $z_i = y_if(x_i)=y_i(w^Tx_i + b)$: $$L(z_i)=\log(1+e^{-z_i}) \tag 2$$    I know that the first one is an accumulation of all samples and the second one is for a single sample, but I am more curious about the difference in the form of two loss functions. Somehow I have a feeling that they are equivalent. "(CRON) info (No MTA installed, discarding output)" error in the syslog How to suppress scientific notation when printing float values? Here's my code:  x = 1.0 y = 100000.0     print x/y   My quotient displays as 1.00000e-05.  Is there any way to suppress scientific notation and make it display as 0.00001? I'm going to use the result as a string. CSH - How to check if input is NOT number Need to apply it on csh.  to check if the inputted $2 is not number nor the word "all"  if ($#argv == 2 &amp;&amp; ($2 != all &amp;&amp; $2 != **any number**)) then    echo "wrong parameter" When I run sudo, what exactly happens to my environment?  When I run sudo command, it doesn't seem to see my or root's environment. For example, my path for both includes /usr/local/bin, but if I try to run one of the program's without the full path, it fails.  I thought sudo ran as root, and hence got root`s environment. Is there a different way that bash executes under sudo than under root or my normal user?  EDIT:  I have been using sudo -i lately, but recently it has been causing problems because my current working directory gets set to /root. This is as expected (sorta), but I still don't understand why sudo isn't recognizing my executables in /usr/local/bin.  EDIT:  I am running Fedora 15. Will some parents be offended when being asked, "Is it male or female?" If I ask the parent about a baby's gender, will it be impolite or not appropriate to say, "Is it male or female?"  Is there any subtle difference, in terms of politeness, among   "Is it a boy or girl?" "Is it he or she?" "is it male or female?"