How can I prove that $\zeta(2n) = (-1)^{n+1}\frac{B_{2n}(2\pi)^{2n}}{2(2n)!}$?
Ways to prove Euler's formula for $\zeta(2n)$
What causes javac to issue the "uses unchecked or unsafe operations" warning How to remove/install a package that is not fully installed? What are your thoughts on writing your text in images?  I'm not saying throughout the whole website... But in certain key locations like image carousels. And I'm not talking about the special cases where you have font types that browsers can't render. I'm talking about text that uses standard fonts and is not too big (3/4 bullets).  Should I embed the text in the images that compose the carousel? Or should I apply the text to the images as "real text" HTML?  What are the advantages/ disadvantages of using text in an image? Can an infectious diseases come from a plant? Coronavirus, HIV, 1918 Flu, etc. They all come from animals. Do any infectious diseases (in humans) come from plants? More specifically, are there viruses that infect plants that can mutate to infect humans? How do I check if an array includes a value in JavaScript? What is the most concise and efficient way to find out if a JavaScript array contains a value? This is the only way I know to do it: function contains(a, obj) {     for (var i = 0; i &lt; a.length; i++) {         if (a[i] === obj) {             return true;         }     }     return false; }  Is there a better and more concise way to accomplish this? I am looking for a story about the future of mankind, in which most people have been enslaved in a virtual reality. It ends with the revelation that the people are just lying there imagining their lives with their heads in a trough of feed.  It explains that chemists began to create compounds that could be released into the air to manipulate citizens - causing them to live, shop, think as desired by whoever was in charge. Eventually these tools got subtle enough that they could simulate reality using just these airborne compounds.  This was clearly a prescient view of what later became computer-based virtual reality fiction. Find the solution of following differential equation:     $$\frac{dy}{dx}=\frac{1}{xy(x^2 \sin (y^2)+1)}$$   Could someone hint me something to get through this problem? Faction Membership Limits in Fallout 4 Are there any limitations to the faction memberships you can have in Fallout 4?  I'm brand-new to the Fallout universe, and just got to the point of being invited to the Brotherhood of Steel. However, I'm a bit concerned about their politics and how it may affect my standing with other factions I may encounter.  If I join the Brotherhood, will there be other factions that I can't join? Are there any other factions that have such limitations?  Note: I'm still not very far into the game, and not very familiar with the Fallout 4 universe in general, so please make liberal use of spoiler markdown in your answers. Essentially, the only things that need to be un-spoilered are Yes/No answers for the questions asked above. I have this string  'john smith~123 Street~Apt 4~New York~NY~12345'   Using JavaScript, what is the fastest way to parse this into  var name = "john smith"; var street= "123 Street"; //etc... Why do I have to click twice to submit a question when Stack Exchange's automated question review has no advice to show? Ideal correspondence I'm confusing the ideal correspondence theorem. Is the following  right?  Ideal correspondence: Let $f:A \to B$ be a ring homomorphism. Then there is a one-to-one order-preserving correspondence between ideals of $f(A)$ and ideals of $A$ which contain $\ker(f)$ by $\alpha \mapsto f(\alpha)$ (conversely $\beta \mapsto f^{-1}(\beta)$), and prime ideals correspond to prime ideals, and maximal ideals correspond to maximal ideals. I have two groups with equal variances and unequal sample size (28 and 8) and I want to run a Student t-test. Can I use Mann-Whitney considering that the variances are equal? Do you think if there is a better test to compare the samples? Any time I am inserting new point feature in QGIS, the Feature Attribute dialog box is popping up. Is there a way to prevent it? (I am willing to insert many points at once and this pop up box slows down the process). iPhone Storage Space Inaccuracy (No Storage Space) How to make the measuring grid larger? When starting the blender, there is always a cube on the floor. The floor is actually a grid. My question is how to make this grid bigger so that we can measure big stuff? Find the number of solutions to $ \lfloor x \rfloor + \lfloor 2x \rfloor + \lfloor 4x \rfloor + \ldots + \lfloor 32x \rfloor =12345$ Find the number of solutions of the equation    $$\lfloor x \rfloor + \lfloor 2x \rfloor + \lfloor 4x \rfloor + \lfloor 8x \rfloor + \lfloor 16x \rfloor + \lfloor 32x \rfloor =12345,$$   where $\lfloor\,\cdot\,\rfloor$ represents the floor function.   My work: I use the fact that $$\lfloor nx \rfloor =\sum_{k=0}^{n-1} \left\lfloor x +\frac kn \right\rfloor.$$ So the equation becomes $$\lfloor x \rfloor +\sum_{k=0}^{1} \left\lfloor x +\frac k2 \right\rfloor +\sum_{k=0}^{3} \left\lfloor x +\frac k4 \right\rfloor +\sum_{k=0}^{7} \left\lfloor x +\frac k8 \right\rfloor   \\ \qquad {}+\sum_{k=0}^{15} \left\lfloor x +\frac k{16} \right\rfloor +\sum_{k=0}^{31} \left\lfloor x+\frac k{32} \right\rfloor   \\ = \lfloor x \rfloor + \left\lfloor x+\frac 12 \right\rfloor + \left\lfloor x+\frac 64 \right\rfloor + \left\lfloor x+\frac{28}{8} \right\rfloor   \\ \qquad {}+ \left\lfloor x+\frac{120}{16} \right\rfloor + \left\lfloor x+\frac{496}{32} \right\rfloor$$  What should I do next? Why is torque a cross product? If I'm not wrong, torque is perpendicular to both the radius and force i. e. It is along the axis of rotation. Questions that arise are- why do we consider the length between the axis/point of rotation while calculating torque? More importantly why is torque a cross product? Addition with NULL values Wiener Process $dB^2=dt$ Why is $dB^2=dt$? Every online source I've come across lists this as an exercise or just states it, but why isn't this ever explicitly proved? I know that $dB=\sqrt{dt}Z$, but I don't know what squaring a Gaussian random variable means. I installed Fedora 15 on my laptop and deleted XP (at least I think XP is deleted).  Then I installed Ubuntu as dual boot with Fedora 15.  Now I want to remove Fedora 15 and leave only Ubuntu (and XP if it is still available).  Can anyone help with the steps to uninstall Fedora?  Please give me simple steps to follow, I'm a nooby.  Thanks!