Why is work done equal to force×displacement?
What is behind the definitions of work and energy?
Methods to compute $\sum_{k=1}^nk^p$ without Faulhaber's formula As far as every question I've seen concerning "what is $\sum_{k=1}^nk^p$" is always answered with "Faulhaber's formula" and that is just about the only answer.  In an attempt to make more interesting answers, I ask that this question concern the problem of "Methods to compute $\sum_{k=1}^nk^p$ without Faulhaber's formula for fixed $p\in\mathbb N$".  I've even checked this  without finding what I want.  Rule #1: Any method to compute the sum in question for arbitrary $p$ is good, either recursively or in some manner that is not in itself a closed form solution.  Even algorithms will suffice.  Rule #2: I don't want answers confined to "only some values of $p$".  (A good challenge I have on the side is a generalized geometric proof, as that I have not yet seen)  Exception: If your answer does not generalize to arbitrary $p$, but it still generalizes to an infinite amount of special $p$'s, that is acceptable.  Preferably, the method is to be easily applied, unique, and interesting.  To start us off, I have given my answer below and I hope you all enjoy. I forgot my iPhone 5 passcode when I was changing the code. A window appeared on the device screen saying that iPhone is disabled.  I have Apple ID and password for it. After signing in to iCloud I have erased the device in order to remove the passcode from my iPhone but it still says that device will be erased when device will connect to internet. What would i have to do? How can I type a Unicode character (for example, em-dash —?) The title pretty much says it all: how can I type Unicode characters - specifically the em-dash —? What would be an appropriate opposite of "exceed"? A word that says a person is both female and your friend Can we have a system to submit potential robo-reviewers for moderators attention? What are the requirements to get the "Weed Eater" hat? The hat's description says     answer a question qualifying for the Tumbleweed badge that gets accepted   During the winter bash, I  a question that is a , and it got accepted; yet I did not get the hat. However  answer  and did get the hat. (What was the difference?)  So what are the exact requirements to get the  hat? I just bought "Reputation to the max". I bought this first, because I really want to help the cleanup of the vote-to-close queue, which, despite the efforts I've been hearing about, is still quite large. According to SO, my reputation is now 15,750, but that queue still says I need at least 3k rep to review! That is clearly a bug! How can I resize an ext root partition at runtime? How can I increase the size of the root partition of a system at runtime?   I have a partition that is not allocated after the root partition (which is also ext4), how can I add that unallocated space to the space allocated to the root partition without having to shutdown the server? Why not to extend the set of natural numbers to make it closed under division by zero? Syntax highlighting in app differs from normal web view Extrusions causing problems in edit mode When I extruded vertices in edit mode, for some reason one of the sides of my 3-D model (the textured-looking side to the right) is creating a lot of errors. First off, it automatically sets extrusions on the x-axis. Secondly, it doesn't allow me to extrude planes into 3-D shapes. Thirdly, I can't increase the height of vertices without it creating a new face. Finally, it renders those automatic textures to create a grainy black texture in render mode. I attached an image with the solid object (top) and the rendered object (bottom). Note: I did not set any textures or alter the lighting on the model. Also, the left gray side is working perfectly fine without errors. Are intermediate rings of finitely generated ring extensions also finitely generated? I often find that I can zoom in to a point, but then cannot zoom any more, even when there is a lot of room to zoom to the meshes on the scene.   This is particularly annoying in the following scenario:  I often land up left clicking on the scene and the 3D cursor shifts there. I use Shift+C to shift the 3D cursor back to the origin. However, this also centers the view on the cursor and shifts the view to show all objects, and sometimes this zooms things way out &ndash; at this point, if I try to zoom in, I can zoom in to a point (using the pinch/zoom on trackpad), but then it stops zooming in.   How do I zoom in after that? Is there anything else I am doing wrong in this case? polar decomposition of a square A when A is not full rank/invertible Integrate $\int \frac{25 - x^2}{x^4} \operatorname d\!x$ Play a short sound in iOS Java method dispatch with null argument What is the domain of $x^x$ as a real valued function? Consider the function $f(x) = x^x$.  Wolfram alpha tells me that this function's domain is $x : x&gt;0$, $x \in \mathbb{R}$. I can't see why it cannot be defined for a number like $(-2)$. I mean $(-2)^{-2}=0.25$, the same Wolfram Alpha told me. I realize that fractional powers for negative numbers may cause problems, but it could be defined for integers. Thanks for any help. Replacing fonts in EPS/PDF files