Facebook Lookback Video
Collage of six photos, not Facebook Lookback movie
how can I find sum of series $ \sum_{n=1}^{\infty} (n\cdot \ln \frac{2n+1}{2n-1} - 1) $? It is so weird for me because I put this to Mathematica and it tells me that sum does not converge...  Let consider sum no to infinity, but to n  $$ \sum_{k=1}^{n} (k\cdot \ln \frac{2k+1}{2k-1} - 1) =$$ $$ ln \frac{3}{1}\cdot \left(\frac{5}{3}\right)^2 \cdot...\cdot \left(\frac{2n+1}{2n-1}\right)^n - n = ln \frac{1}{1}\cdot \frac{1}{3}\cdot \frac{1}{5}\cdot ... \frac{1}{2n-1} - n $$ but $$ n = ln e^n $$ so it will be $$ln\frac{1}{e^n} \cdot \frac{1}{1}\cdot \frac{1}{3}\cdot \frac{1}{5}\cdot ... \frac{1}{2n-1}$$  So the limit of it is $-\infty$ Have I done this well or I missed sth? Assume two black holes in the most common size range, spiraling into each other until they merge. The event releases significant amounts of energy via gravitational waves, which warp the space-time.  If the distortion is powerful enough, it would get noticed in daily life, or perhaps even detected by the proprioceptors in the human body.  How close, as an order of magnitude estimate, would you have to be to the merger to perceive it like that, without any instrument? What is the probability that all three tosses result in the same outcome? A coin is tossed three times: The probability of zero heads is 1/8 and the probability of zero tails is 1/8.  And my question is: What is the probability that all three tosses result in the same outcome?   So, if P(zero heads)= 1/8 , then that should be the same of p(all tails)?  If so, we could use the Addition Rule which is $P(A \cup B) = P(A) + P(B)$  where A and B are disjoint events, i.e. $A \cap B = \emptyset$, A is the event of tossing all heads and B is the event of tossing all tails.  I'm not sure how to continue after that... would the complement be used? Some publications capitalize He, Him, etc., when referring to a god.    What is this practice called? 'Proper noun' is rather generic. every permutation is either even or odd,but not both How we can show every permutation is either even or odd,but not both......I can't arrive at a proof for this ..... Can anybody give me the proof...  Thanks in advance... I just created a plane and added a wave modifier to it, to simply make it look like something fluid. Now, I have an Object that I want to place on the surface of this fluid plane. But how do I do that?  I thought of adding a driver to my Objects location, but I have no clue how to get the location of a certain vertex in runtime. MariaDB won't start on Ubuntu: Can't lock aria control file Can an illusion give a player partial cover? I'm in an argument with a player at my table, he says hiding behind some bushes while shooting arrows at my monsters gives him partial cover because they can only see his head and shoulders. So they're limited in what they can even aim at. I accepted that. And now he's trying to use minor illusion to create fake bushes/walls and continuing to claim he has partial cover.  I thought cover was based on having a solid obstacle between you and the target... Like, if a magical attack, or penetrating attack can pass through your cover, wouldn't that negate the AC bonus from partial cover? Or is it about "aiming"? Ignore folders/files when Directory.GetFiles() is denied access I am trying to display a list of all files found in the selected directory (and optionally any subdirectories). The problem I am having is that when the GetFiles() method comes across a folder that it cannot access, it throws an exception and the process stops.  How do I ignore this exception (and ignore the protected folder/file) and continue adding accessible files to the list?  try {     if (cbSubFolders.Checked == false)     {         string[] files = Directory.GetFiles(folderBrowserDialog1.SelectedPath);         foreach (string fileName in files)             ProcessFile(fileName);     }     else     {         string[] files = Directory.GetFiles(folderBrowserDialog1.SelectedPath, "*.*", SearchOption.AllDirectories);         foreach (string fileName in files)             ProcessFile(fileName);     }     lblNumberOfFilesDisplay.Enabled = true; } catch (UnauthorizedAccessException) { } finally {} How can one request reconsideration of a   after a certain period of time, let us say after one year? Map not loading when using getLegend and showing error for getView() I was able to run my application on using Legend earlier but now I want to update my Legend when scrolling on the map. So I tried to used this code  . And I got the gist of how he is able to do that but when I am trying the same I keeping getting the error var graphicUrl = wmsSource.getLegendUrl(currentResolution);  I think this is mainly due to the wmsSource not declare. But I tried to initialize  seems wmsSource in TileWMS but does not seems to work. var getExtent = function () {     return map.getView().calculateExtent(); } var getProjectionCode = function () {     return map.getView().getProjection().getCode(); }  var updateLegend = function() {     var currentResolution = map.getView().getResolution();     var graphicUrl = wmsSource.getLegendUrl(currentResolution);        const crs = `&amp;CRS=${getProjectionCode()}`;     const bbox = `&amp;BBOX=${getExtent().join(',')}`;     const height = getHeight(getExtent());     const width = getWidth(getExtent());     const heightAndWidth = `&amp;srcwidth=${height}&amp;srcheight=${width}` ;     const legenOptions = &quot;&amp;legend_options=countMatched:true;fontAntiAliasing:true;hideEmptyRules:true;forceLabels:on&quot; ;        var img = document.getElementById('legend');     img.src = `${graphicUrl}${crs}${bbox}${heightAndWidth}${legenOptions}`; }; //Updated Legend End   //View var myview = new ol.View({     center : [8717490.201868,2788422.791843],     zoom : 4 })  var firstSel = document.getElementById(&quot;City&quot;); var secSel = document.getElementById(&quot;Sector&quot;);  //var LayerArray = [baseLayer, firstLayer]  //Map var map = new ol.Map({       target : 'mymap',       view: myview,       layers: [         new ol.layer.Tile({             source : new ol.source.OSM({                 attributions: 'Surveyor Allpication'             })         }),         new ol.layer.Tile({             source : new ol.source.TileWMS({                url: 'http://localhost:8089/geoserver/India/wms',                params: {'LAYERS': 'India:India', 'TILED': true,'TRANSPARENT':true},                ratio: 1,                serverType: 'geoserver',                transition: 0,             })         })       ] }) updateLegend();   This here is my JS &lt;div class=&quot;innerMap&quot;&gt;     &lt;div class=&quot;map&quot; id=&quot;mymap&quot;&gt;&lt;/div&gt;         Legend:     &lt;div&gt;&lt;img id=&quot;legend&quot;/&gt;&lt;/div&gt;     &lt;!--    &lt;div&gt;&lt;img src=&quot;http://localhost:8089/geoserver/wms?REQUEST=GetLegendGraphic&amp;VERSION=1.0.0&amp;FORMAT=image/png&amp;WIDTH=20&amp;HEIGHT=20&amp;LAYER=India%3AIndia&amp;RULE=Agra&quot; /&gt;%Name&lt;/div&gt; --&gt; &lt;!--    &lt;div&gt;&lt;img src=&quot;http://localhost:8089/geoserver/India/wms?SERVICE=WMS&amp;VERSION=1.1.1&amp;REQUEST=GetLegendGraphic&amp;FORMAT=image/png&amp;WIDTH=20&amp;HEIGHT=20&amp;LAYER=India%3AIndia&amp;SRS=EPSG%3A4326&amp;STYLES=&amp;SRCWIDTH=742&amp;SRCHEIGHT=768&amp;BBOX=75.4541015625%2C14.21630859375%2C91.7578125%2C31.09130859375&amp;LEGEND_OPTIONS=countMatched:true;fontAntiAliasing:true;hideEmptyRules:true&quot; /&gt; &lt;/div&gt;  --&gt;     &lt;/div&gt;  This is my HTML. How do I make this work? Observed and Observable What is observed and what is observable? I found this two word frequently in the context of random variable and realization of random variable.  What is the difference between observed and observable? Is it possible to extend a tourist Schengen visa (12 more days)? Squid IP Routing Issue I have a squid server installed with 30 additional proxy addresses. Whenever I try to use one of these proxy addresses with a browser, like chrome, my IP shows as the main server IP as opposed to the additional address. For example, say the home IP is 192.0.0.10 and the additional IP I'm trying to use is 192.0.0.13, when going to a &quot;what is my IP&quot; type of site, it shows 192.0.0.10 no matter what additional address I use. Any idea as to why this might happen? Thanks for any help. Group theoretic meaning of natural isomorphisms between certain functors So imagine you have a group $G$ and we consider the set of group homomorphisms from $\mathbb{Z}$ to  $G$ specified by  $\forall g$ $\in G$ $\exists$   $\phi(1)=g$. Each of these homomorphisms is in 1-1 relation with the elements of $G$.  Consider groups for a moment in the context of category theory, viewing the groups as one object categories and thereof group homomorphism as functors. What would a natural isomorphism mean in group theory terms for G?  My thoughts are that the natural transformations equate to maps between homomorphisms and since the homomorphisms are in 1-1 relation with the elements of G, then a natural transformation is a map between group elements, i.e another element of the group. I'm not entirely convinced by this.   Anyway continuing my reasoning a natural isomorphism is a map between the homomorphisms that has an inverse, the thing is in relation to the elements of G this is every element? Furthermore I'm looking to find an equivalence class defined by this natural isomorphism, is this just a collection of the elements that are each others inverses?  Thanks in advance for any assistance. Select Input Texture file name as parameter/node I am trying to create a material node group for triplanar mapping, but I am not sure how I can parameterize the image texture name.   I have 3 image texture nodes, which all use the same file with the same settings, the only difference is the vector input.  Is there a way I can make it so that I only have to select the texture name once, possibly as a input for a group? URLs are linked despite being inside a code span My Notes has Title-Task2 and Content is "Talk to customers"  When I run following query:  SELECT Title,Content FROM ContentNote  Output is:  ('Title', 'Task2'), ('Content','/services/data/v42.0/sobjects/ContentNote/0692x000000WFDKAA4/Content')])]  how to get my actual content from this? What is the difference between "used space", "size" and "size on disk"? There is only one partition for both system files and personal data, which is C:. The other two partitions are for boot and for recovery.  Now I have two different reports on the size of C: on my Windows 7:   by clicking the property of C:, it shows 59.4 GB for "used space"; by selecting all contents (I have setup to view all hidden files and directories) under C: and viewing their property, it shows 46.9 GB for "size" and 47.6 GB for "size on disk".   Here are my questions:   I was wondering why the two reports are not the same, and where the difference comes? in the second way, why "size" and "size on disk" are different? What do they mean actually? What is the difference between them and "used space" in the first way?   Thanks in advance! I have been trying to show these two inequalities hold for all positive integers n, but I don't know how to proceed at all... I have tried playing around with them but I didn't find anything helpful. I have also tried induction but I couldn't make it work.