Coefficient of x^50 in the cube of a summation
Find coefficient of $x^{50}$ in $(\sum_{i=1}^{\infty}x^n)^3$
What is the proof that the total number of subsets of a set is $2^n$? Parsing domain from a URL I need to build a function which parses the domain from a URL.  So, with   http://google.com/dhasjkdas/sadsdds/sdda/sdads.html   or  http://www.google.com/dhasjkdas/sadsdds/sdda/sdads.html  it should return google.com  with   http://google.co.uk/dhasjkdas/sadsdds/sdda/sdads.html  it should return google.co.uk. I'd really like to learn how to play pen-and-paper RPGs.  I know that it takes a few players to actually sit down and play, but I'm not at all sure where to find more gamers.  How do I find existing groups to join? Or, are there any resources online that may help me find existing RPG groups or players? Proof that the largest eigenvalue of a stochastic matrix is $1$ The largest eigenvalue of a  (i.e. a matrix whose entries are positive and whose rows add up to $1$) is $1$.  Wikipedia marks this as a special case of the , but I wonder if there is a simpler (more direct) way to demonstrate this result. I would like to solve the beginner's standard exercise which claims that a point of $\mathrm{Spec} \ R$ is closed iff it is a maximal ideal.  The reverse implication is easy. The direct one seems much subtler. If $P = V(I)$ then, since there exist a maximal ideal $M$ containing $P$, it would follow that $\{P, M\} \subseteq V(I) = P$, whence $P=M$. In order to show the existence of $M$ I applied Zorn's lemma to the set of ideals containing $P$.  The question is the following: is there any other proof of the above implication that does not (indirectly) use the axiom of choice? My concern is that I may be using a cannon to shoot a fly. Also, it would be the first time that I see closedness of points to require the axiom of choice. If the axiom is indeed needed in general, are there "nice" classes of rings for which we could get away without it? How to add a Timeout to Console.ReadLine()? How can I retrieve data within my widget I have a Widget which I am creating but my quesiton is how do I access my custom table which I created via my plugin. I am attempting to fill the dropdown from the table called tfp which contains the column liters which I wish to popluate the values into the drop down   class my_plugin extends WP_Widget {  // constructor function my_plugin() {         parent::WP_Widget(false, $name = __('Thomsons Fuels Widget', 'wp_widget_plugin') );  }  // widget form creation function form($instance) {  //Check values if( $instance) {  $title = esc_attr($instance['title']);  $dropdown= esc_attr($instance['dropdown']);  $textarea = $instance['textarea'];  } else {  $title = '';  $textarea = ''; } ?&gt;   &lt;p&gt; &lt;label for="&lt;?php echo $this-&gt;get_field_id('dropdown'); ?&gt;"&gt; &lt;?php _e('Liters',   'wp_widget_plugin'); ?&gt;&lt;/label&gt; &lt;select&gt; &lt;option value="volvo"&gt;Volvo&lt;/option&gt; &lt;/select&gt;  &lt;/p&gt;   How I created the table in the plugin   global $wpdb; global $custom_table_example_db_version;  $table_name = $wpdb-&gt;prefix . 'tfp'; // do not forget about tables prefix  // sql to create your table // NOTICE that: // 1. each field MUST be in separate line // 2. There must be two spaces between PRIMARY KEY and its name //    Like this: PRIMARY KEY[space][space](id) // otherwise dbDelta will not work $sql = "CREATE TABLE " . $table_name . " (   id int(11) NOT NULL AUTO_INCREMENT,   liters VARCHAR(100) NOT NULL,   price VARCHAR(100) NOT NULL,      postcodearea varchar(20) NULL,         dft varchar(20) NULL,   PRIMARY KEY  (id) );";  // we do not execute sql directly // we are calling dbDelta which cant migrate database require_once(ABSPATH . 'wp-admin/includes/upgrade.php'); dbDelta($sql);  // save current database version for later use (on upgrade) add_option('custom_table_example_db_version', $custom_table_example_db_version); I have an Excel file that has a bunch of VBA and macro code in it.  When I open the file in Excel I can choose not to 'enable' them - so the values in the fields all stay as they were during the last save.  I need to manipulate the values as they were last saved - so I don't want the macros (which look at the current date and update values accordingly) to run.  When I open it via our dot net code:   Dim oxlRep As Excel.Application Dim oWBRep As Excel.Workbook Dim oSheetRep As Excel.Worksheet Dim oRngRep As Excel.Range oxlRep.Open(path)   the vb code runs - throwing off the values.  I've been looking for a way to open it without macros, or in 'secure' mode where the macros aren't run.  If I simply double click the file and don't choose to enable macros the values are all there as I want them.    Usually we run this code within the month that the files are created, so we haven't seen this problem in the 3 or 4 years that it has been working.  Now I need to go back to some of the old files and run some archival code...    Anyone have a suggestion? Animations about a young man pulled into a fantasy setting with dragons? I'm looking for an animation (more likely a film not a series) that I watched as a kid, watched early 90's I'm sure it contained a book loving male main character (wears glasses might have even had an amulet) who gets pulled into a fantasy via a magic book  Setting with dragons and an evil wizard, I remember it being on TV as I never had it on VHS.  Same sort of animation technique as visionaries or thundercats.  Thanks. Could the Horcruxes be destroyed with Avada Kedavra? In The Deathly Hallows Hermione says this about destroying Horcruxes:     “It doesn’t have to be a basilisk fang,” said Hermione patiently.   “It has to be something so destructive that the Horcrux can’t repair   itself. Basilisk venom only has one antidote, and it’s incredibly   rare—"      "That’s a problem we’re going to have to solve though, because ripping, smashing, or  crushing a Horcrux won’t do the trick. You’ve got to put it beyond magical repair.”   Mad-Eye Moody from The Goblet of Fire tells us this about Avada Kedavra,     ...there's no countercurse. There's no blocking it.   but also that,      Avada Kedavra's a curse that needs a powerful bit of magic behind it - you could   all get your wands out now and point them at me and say the words, and I doubt   I'd get so much as a nosebleed.    Harry is also seen once attempting to use Crucio on Bellatrix Lestrange in The Order of the Phoenix out of anger at the death of Sirius, but he fails. She tells him,     "You need to mean [Unforgivable Curses], Potter! You need to really want to cause pain - to enjoy it - righteous anger won't hurt me for long - I'll show you how it is done, shall I? I'll give you a lesson -"   Even if Harry and company are not powerful enough to perform the curse themselves, they know several powerful wizards (Kingsley, Lupin, et al.) who could likely perform the curse.  Lastly we know that Voldemort himself destroyed the last bit of his soul that was inside Harry with Avada Kedavra.  Could the Horcruxes be destroyed with Avada Kedavra as well? How to create a .deb file with dependency? I have a game made with the LÖVE framework and I want to package it into a .deb file so it can be easily installed by others and be easily findable through the Unity dash for example.   I also have the LÖVE framework love_0.7.2.deb which I want to be in the deb file also somehow.  Files that I have:  game_icon.png game .desktop the_game.love love_0.7.2.deb   Could someone explain to me how to do this? I recently setup a new computer for my parents with windows 10 home. I made two local accounts for them - no microsoft accounts. I also would like to keep them without a password. Problem is now that windows automatically signs in with the last used account. No lock/login screen.  I tried a number of answers from similar questions here but none worked. Since it's a home version there are no group policies and the method using task scheduler does not work because accounts with no password are not allowed to create such tasks.  Are there other options to force windows to show a user list on startup without setting passwords for the accounts? How does Linux kernel compare to microkernel architectures? I read once that one advantage of a microkernel architecture is that you can stop/start essential services like networking and filesystems, without needing to restart the whole system. But considering that Linux kernel nowadays (was it always the case?) offers the option to use modules to achieve the same effect, what are the (remaining) advantages of a microkernel? How to completely disable auto-save and versions in Mac OS X Lion? I hate the automatic saving and versioning in Mac OS X Lion.  Is there a way to completely turn it off?  (This has been asked before , but the answer and the linked article are completely wrong, so I thought I'd try again.) How to watch Youtube fullscreen on one monitor of a dual-monitor display? How to watch Youtube fullscreen on one monitor of a dual-monitor display, in Linux?  If I do it in Google Chrome, as soon as I do anything at the other monitor, Chrome jumps back to normal window.  Edit: added that OS is Linux. How can I wake-up a PC using a command? (i.e. equivalent to moving a mouse, etc) It doesn't seem like this would be very difficult, but how can I wake-up a PC by doing the equivalent of moving a mouse or pressing keys on a keyboard?  My PC is running Windows 10 and I only have the monitors enter sleep mode after 15 minutes.  The rest of the PC is still awake and doesn't use hibernate, etc.  I'm trying to use EventGhost to receive a TCP/IP command that tells the PC to wake up the displays but it's proving quite difficult. Is it possible to disable the 'Block Placed' message when using tellraw /setblock? I want to make a tellraw shop but to activate command blocks I want to use /setblock command when clicked on a text. Is it possible to disable "Block placed" text showing up? How to fill gaps in SLC-Off Landsat 7 ETM+ Images with QGIS? Explanation of the problem:     On 31 May 2003 the Landsat 7 Enhanced Thematic Mapper (ETM+) sensor had a failure of the Scan Line Corrector (SLC). Since that time all Landsat ETM+ images have had wedge-shaped gaps on both sides of each scene, resulting in approximately 22% data loss. These images are available for free download from the USGS GloVis website and are found in the L7 SLC-off collection.   source:   Can I use Qgis instead of proprietary software (ENVI, Erdas....) to fill the gaps? How to get IOS "tossing feature" in Wolfram IOS Player to work in Mathematica Why is the subject omitted in sentences like "Thought you'd never ask"?