What is the value of the sum $$\sum\limits_{n=0}^{\infty}(-1)^{n-1}\frac1{(2n+1)^3}$$ I think the sum evaluates to $\frac{7\zeta(3)}{8}-\frac1{32}\zeta(3,-\frac1{4})$, where the last zeta is the Hurwitz zeta function. But, Hurwitz zeta is defined only for $\operatorname{Re}(q)&gt;0$ as a Dirichlet series in this manner. Am I right? Any hints? Thanks beforehand.
Prove that : $$\sum_{k=0}^{\infty} \frac{(-1)^{k}}{(2k+1)^3}=\frac{\pi^3}{32}.$$    I think this is known (see ), I appreciate any hint or link for the solution (or the full solution).
What if client doesn't like any logo design concept? I'm in a process of creating Graphic Design contract. I've decided to provide each client with 3 logo concepts and 3 rounds of revision. Ideally, I would create 3 concepts and client will chose one, but it happend to me before that client didn't like and concept and I end up with doing 10+ more (yes, I've worked without contract).  How can I prevent this situation? Should I charge hourly for each new concept separately? How can I express my thoughts clearly in a contract (without sounding like 'if you don't like any, you'd have to pay more)? I don't want to scare client and put thoughts into their minds saying that there is a possibility that they won't like me ideas. Flex HTTPservice and POST, Sending Files? I use a basic Post to send data to a Django server.  The data consists of a base64 encoded 640*380 PNG image dynamically created by the flex component.  &lt;mx:HTTPService id="formSend" showBusyCursor="true"      useProxy="false" url="http://127.0.0.1/form/"      method="POST" result="formSentConfirmation(event)"    fault="formSendingFailed(event)"/&gt;    private function sendForm(url:String, message:String, meteo:Number):void {     formSend.url = url;     var params:Object = { message: message, image_data: getEncodedImage() };      snapButton.label = "sending ...";     formSend.send(params); }   On the server side i can see that the data is in the request.POST not in request.FILES. That means the image is not send as a File with multiencode HTTP.   Will i get into trouble on a real server ? since the limit is 200k for urlencoded POST var. How to make HTTPservice send the data as a file? Any other solutions?   Thanks A dollar amount $\${-}67.9{-}$ is divisible by 72. What is this number? A client buys 72 turkeys. On the receipt, 2 digits are missing, the first and the last. So, the total price is $\${-}67.9{-}$. Find a way to make the price of each turkey round at the second digit without trial-and-error method.  So, the answer is obviously $\$5.11$/turkey, so $\$367.92$ total. I found that with with 2-3 trial-and-error.  I bypassed his problem by using python and made a script that tries every combination and assures it is divisible by 0.01.   Please help me find a mathematical way of solving this problem. Looking to draw this block diagram in Tikz I'm looking to create something like this in Tikz environment. Any tips? help? I have decided to switch from Powerpoint to Beamer, and for my first presentation I'd like to use the , and the same colors as in this goggle slide template:  .  I tried to do some research about it, the closest answers I found are the question  and the . I tried this code:  \documentclass{beamer} \usepackage[frenchb]{babel} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc}  \usetheme{metropolis}  \definecolor{bluegreen}{rgb}{3, 166, 155} \definecolor{pitchblack}{rgb}{0, 0, 0} \definecolor{lightbeige}{rgb}{255, 251, 241} \definecolor{mediumgray}{rgb}{183, 183, 183}  \setbeamercolor{background canvas}{bg=pitchblack} \setbeamercolor{normal text}{fg=lightbeige} \setbeamercolor{headline}{bg=bluegreen, fg=mediumgray}  \begin{document} \begin{frame}     \frametitle{The title}     Lorem ipsum... \end{frame} \end{document}   I does everything I want, except that the title bar's background color is lightbeige:    What did I do wrong? Or what argument should I pass to \setbeamercolor to get it right? Thanks in advance :-). How do I enable or disable the global application menu? What is the difference between the examples below?  Generally, in a newspaper, news is based on past tense (things which have already happened).   Then why are headlines written in ways that says: He Kills (shouldn't it be: He Killed)?  For example:  Parliament passes bill vs. Parliament passed bill  Also  He kills his friend vs. He killed his friend  Please help. How do I clean the inside of my viewfinder? My viewfinder (not LCD) has spots of dust on it.  What is the best way to clean the inside?  I have cleaned the outside with a QTip. I need to build a probabilistic cellular automaton for simulating land-use changes and am wondering how to implement this in a GIS. I understand that Markov chains are a way of doing this, and IDRISI has some sort of module for Markov chains, but I have no access to IDRISI.  that, with raster data, this can, in theory, be done with any GIS that can do raster algebra. Presumably this means that it can even be done in ArcGIS, and I think I've figured out how to build cellular automata in ModelBuilder (once I know with certainty how to make iteration work there).  Still, I can find next to no practical advice on this. Once I have two datasets, one showing the land use at a certain point in time (time A) and the other at a later time (time B), I imagine doing the following (correct me if I'm wrong):   If there are (for example) 3 types of land use, then there are 9 possible things that can happen to a cell from time A to time B; thus, reclassify each dataset such that each land use is represented by a different number (for example, 9, 11, and 14 at time A and 3, 4, and 5 at time B); Divide one raster by the other, obtaining a raster with 9 possible cell values. Determine the percentage of cells in the new raster that has each of the 9 values (I forgot, how does one do this in ArcGIS?); those will be the probabilities of each type of change (or lack thereof) in land use.   What I cannot figure out, though, is how to apply these probabilities during the next iteration. Finally, I wonder if there is a way of making an external factor (say, proximity to roads) influence the spatial distribution (not the overall likelihood) of change in my model.  Can anyone recommend where to find information on how to do this in ArcGIS? Bag A has $3$ white and $2$ black marbles. Bag B has $4$ white and $3$ black marbles.  Suppose we draw a marble at random from Bag A and put it in Bag B. After doing this, we draw a marble at random from Bag B, which turns out to be white. Given this information, what is the probability that the marble we moved from Bag A to Bag B is white?  At first since the probability that white is $1/2$ is $2/5$, and the probability that white is $5/8$ is $3/5$, I thought a sufficient answer would be $$\begin{align}\tfrac 1 2 \cdot \tfrac 2 5 + \tfrac 5 8 \cdot \tfrac 3 5 &amp; = \tfrac 1 5 + \tfrac 3 8 \\ &amp; = \tfrac 8 {40} + \tfrac {15}{40} \\ &amp; = \tfrac {23}{40}\end{align}$$, but that was wrong.   Can someone provide me with an answer? Thanks Cannot turn Bluetooth off How does temperature relate to the kinetic energy of molecules? In ideal gas model,  is the measure of average kinetic energy of the gas molecules. If by some means the gas particles are accelerated to a very high speed in one direction, KE certainly increased, can we say the gas becomes hotter? Do we need to distinguish the random vibration KE and KE in one direction?  Furthermore, if we accelerate a block of metal with ultrasonic vibrator so that the metal is vibrating in very high speed with cyclic motion, can we say the metal is hot when it is moving but suddenly become much cooler when the vibration stop? Some time ago, I baked a cake (Sachertorte to be exact). The taste and texture was fine, so my recipe is okay.  My biggest issue was the shape. In the middle it was really a lot higher than on the sides. I would like to redo it in the near future, but preferably with a flat(ter) surface. (Especially since I put icing on top and I don't want it to drip off this time.)  Anyone knows the cause of my problem, or even better a solution? I think I put enough butter on the side of my springform pan, in case this is an option. Where do I use delegates? What are some real world places that call for delegates?  I'm curious what situations or patterns are present where this method is the best solution.  No code required. Cross product term in linear regression why is it zero I'm trying to see why this is the case. I have taken  the LHS and added $X\hat{\beta}$ and subtracted $X\hat{\beta}$.  From this I can get both terms on the right but I end up with a cross product term  $2(y-X\hat{\beta})^T(X\hat{\beta} - X\beta)$  that I can't prove equals to zero. I think there is some trick I'm missing, anybody remember it? Getting the array length of a 2D array in Java How do I go about porting Ubuntu Touch to different devices? My Android device won't connect. I've never got MTP to work, I've only ever got it to connect by USB mass storage, which was how it was working most recently. But now, since 13.04, it seems that option has been taken away entirely.  I need to be able to connect by USB to transfer files.  When I plug in the device I get an error that says Unable to open MTP device '[usb:002,003]':    After some web searching, I found that I might need a program called go-mtpfs, so I tried that, and it failed:  $ go-mtpfs /media/MyAndroid 2013/07/16 16:41:43 compiled against libmtp 1.1.5 Device 0 (VID=04e8 and PID=685e) is a Samsung Galaxy Y. 2013/07/16 16:41:43 found device Samsung: Galaxy Y (04e8:685e) @ bus 2, dev 3 :  LIBMTP PANIC: Unable to find interface &amp; endpoints of device 2013/07/16 16:41:43 rdev.open failed: open: open returned nil   How do I get my USB device to just connect, automatically, like it used to? Is there a word for someone that always has to be right? The person gets angry if they are not. Is there anyway to restore the Blender default Cloth settings? Or is there anyway to find what the default settings are?  I didn't realize at the time that by changing the values I was overriding the default values.  Using Blender v2.76.