Proof verification for proving $\forall n \ge 2, 1 + \frac1{2^2} + \frac1{3^2} + \cdots + \frac1{n^2} < 2 − \frac1n$ by induction
Proving $ 1+\frac{1}{4}+\frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$ for all $n\geq 2$ by induction
Power Supply Capacity Formula Updating the repository isn't working When I run sudo apt-get update get this output:   sudo apt-get update E: Type '&lt;!DOCTYPE' is not known on line 1 in source list /etc/apt/sources.list.d/playonlinux.list E: The list of sources could not be read.   Also Ubuntu software Center is not opening. What happens if you use a Clone Effect on a Double Faced Card that's Transformed? Say someone has , which is a 0/3 Defender, and after some mechanics, transforms into a 13/13 Lizard Horror with Trample.  Say this someone managed to transform said card into its 13/13 Trample form, and then cast  on it (or any other clone type card if it would matter between different ones). Does the Metamorph/Clone/etc. come into play transformed, or as the 0/3 Defender? How to only append to clipboard (but not overwrite current data)? I have a rather large file, I need to copy the entire contents somewhere, but when I scroll down the page all the data I have selected becomes unselected. I could just copy and paste block by block, but I would find it much easier as there is a lot of data, to just be able to append the contents to the end of the current clipboard data. Is that possible?  That is so that I can have a keyboard shortcut which will enable me to copy this to the clipboard:  I am some nice new text.   When this is what is already there:  I am the old text.   And have it look like this when pasted:  I am the old text. I am some nice new text.   So there are 3 things that I would really like from this (I would have 3 separate keyboard shortcuts to do this):   Append the data to the end of the clipboard and have it put in a RETURN before it (as shown in the example above). Append the data to the end of the clipboard but have it so that there is not RETURN before it so that it would continue on on the same line initially. Have all this but so that the data is put at the beginning of the clipboard before all the data which is currently there.   I am running Ubuntu GNOME 16.04 with GNOME 3.20. Why are doctors addressed as Mr. in the UK? In the US most physicians, surgeons and dentists are addressed as "doctor". Very few other professionals receive the same title.  In the UK, however, surgeons and dentists seem to prefer to be referred to as Mr. If that is true, why?  And who is addressed as Dr. in the UK?  Those who hold doctoral degrees only? Does there exist a holomorphic function with the following property? My  objective is to classify sensor signals.  The concept of my solution so far is : i) Engineering features from raw signal ii) Selecting relevant features with ReliefF and a clustering approach iii) Apply N.N, Random Forest and SVM  However I am trapped in a dilemma. In ii) and iii), there are hyperparameters like k-Nearest Neigbours for ReliefF or the window length, for which the sensor signal is evaluated, or the number of hidden units in each layer of N.N.  There are 3 Problems I see here : 1) Tuning feature selection parameters will influence the classifier performance 2) Optimizing hyperparameters of classifier will influence the choice of features. 3) Evaluating each possible combination of configuration is intractable.  So my questions are : a) Can I make a simplifying assumption, s.t. tuning feature selection parameters can be decoupled from tuning classifier parameters ? b) Are there any other possible solutions ? Can someone help me figure out the big-O for the recurrence relation $T(n) = T(n^{1/2}) + 1$?  I didn't think the master theorem would work since it requires $T(n) = T(n/b)$... to have $b$ as a constant. I was wondering if anyone could shed some light on a method to approach this problem? (not looking for a solution) How to make a traditional division How to make the traditional division? Like that:  a |b_ r  c FFmpeg - Apply blur over face Some Windows 10 UWP icons not displaying on search, or in settings Solve the equation $28^x = 19^y+87^z$ in integers Uncheck checkboxes by changing particular checkbox state I have custom fields in contacts form named checkbox1__c, checkbox11__c, checkbox12__c, checkbox13__c.  When I check checkbox1__c then I want checkbox11__c,  checkbox12__c,  checkbox13__c to be unchecked.  When I unchecked checkbox1__c then I want checkbox11__c, checkbox12__c, checkbox13__c to be checked.  Is there any way to do this by using validation-rules? If not no way to this by validation-rules, then what is the best way to do this? Terminal flashes on empty backspace with Yosemite Since using Yosemite, I've had the annoying problem of my current Terminal window flashing when backspacing on an empty line. I know on previous versions of OS X this flashing was not default, and could be toggled in accessibility settings, but I cannot find the same setting and I'm dying to get this turned off. Any known ways to get rid of it? Could a website force the browser to go into fullscreen mode? The difference between "Older" and "Elder" What is the difference between "Older" and "Elder" ?  And are they interchangeable ? Capturing URL parameters in request.GET I am currently defining regular expressions in order to capture parameters in a URL, as described in the tutorial. How do I access parameters from the URL as part the HttpRequest object? My HttpRequest.GET currently returns an empty QueryDict object. I'd like to learn how to do this without a library, so I can get to know Django better. Order a MySQL table by two columns How do I sort a MySQL table by two columns? What I want are articles sorted by highest ratings first, then most recent date.  As an example, this would be a sample output (left # is the rating, then the article title, then the article date)  +================+=============================+==============+ | article_rating | article                     | article_time | +================+=============================+==============+ | 50             | This article rocks          | Feb 4, 2009  | +----------------+-----------------------------+--------------+ | 35             | This article is pretty good | Feb 1, 2009  | +----------------+-----------------------------+--------------+ | 5              | This Article isn't so hot   | Jan 25, 2009 | +================+=============================+==============+  The relevant SQL I'm using is: ORDER BY article_rating, article_time DESC  I can sort by one or the other, but not both. Extrude Faces along Local Normals I am trying to extrude faces of a cylinder along local normals. 3dsmax can do it easy, couldn't find how to do it in blender.  The extrude region option extrudes it as shown in the first example. I want it done like the 2nd example. GameJolt is a gaming platform/website that offers API access with features like achievements tracking for users, etc. I can use the API no problem on my tests but what I'm concerned about is the private key that is issued to my game. How do I ensure that it's protected from people that want to decompile my game? Once  they get the API private key, they will be able to do anything with it.