Sum $\frac{1}{2} + 1 + \frac{9}{8}+1+\frac{25}{32}+\frac{36}{64}+\cdots$
How to obtain the sum of the following series? $\sum_{n=1}^\infty{\frac{n^2}{2^n}}$
Can the Next/Prev Post links be ordered by menu order or by a meta key? I have a series of posts that are ordered by a meta_key value. They could also be arranged by menu order, if necessary.  The next/prev post links (generated by next_post_link, previous_post_link, or posts_nav_link all navigate by chronology. While I understand this default behaviour, I don't understand how to change it. I found that it maps through to adjacent_post_link in link-template.php, but then it starts to seem fairly hard-coded. Is it recommended to re-write this from scratch to replace it, or is there a better solution. What is an effective way to level Archery? Problems with Groups in Traminer I'm having a problem using the group function in TraMineR. I have a data set that contains SPELL data, so multiple rows per case. I also have demographic data per case, at one row per case. I merge these together and end up with data that has a demographic covariate per row, so multiple rows per case. An example of this data would be:  id startmin stopmin activity educ4 4      1      20       work    HS 4      20     40       play    HS 8      1      15       sleep   College 8      15     40       work    College   I can make sequence data from this, but when I try to run a plot using the group command        seqiplot(atus.seq, group = atus.seqdata$educ4, border=NA,                 withlegend="right",  cex.plot=.55)   it tells me:       &gt;"Error: group must contain one value for each row in the sequence object".   I have gotten this to work with the example of the mvad data in the training manual, but I can't seem to get it to work with the groups, whether I link to the original demographic data, the merged data, or try to pass the covariates by seqformat and seqdef. Ideas? How to allocate aligned memory only using the standard library? How to assign the result of the previous expression to a variable? Is spell level a character concept or a player concept? Is there anything in RAW that supports spell level as a character concept, or alternatively that supports it as solely a player concept?  On the one hand, I see nothing that explicitly states that a character knows that there are spell levels. On the other hand, I don't see how a spellcaster could manage spell slots without knowing about spell levels. What is the rule to convert the 'mm' notation to the 'optical zoom' notation? I searched a bit and found this one:  optical zoom = maximum focal length / minimum focal length   For example a 18-55mm lens would have a 3x optical zoom, and a 18-200mm lens would have a 11x optical zoom. Is that right? no match for ‘operator<<’ in ‘std::operator Why is my Mac constantly trying to connect to another server? After logging on, I see this dialog box pop up. Whenever I dismiss it, it reappears 30 seconds later. (Stealing focus at the same time! Grrrr!)    "Slate" is my old iMac, which is sitting on the desk next to me, turned off. How can I stop my new Mac from constantly trying to connect to my old one? Both are running 10.7.1. Permalinks: custom post type -> custom taxonomy -> post I am having trouble working with WordPress rewrite rules, and could use some help.  I have a custom post type called _shows_.  All shows have a single custom taxonomy category _show-category_. A _show_ will never have more than one _show-category_.  I would like my urls to route in this manner:  www.mysite.com/shows/  =&gt;  archive-shows.php  www.mysite.com/shows/%category%/ =&gt; taxonomy-show-category.php  www.mysite.com/shows/%category%/%postname%/ =&gt; single-shows.php   So as a real world example, lets say we have a _show-category_ "Foo" and a _show_ post titled "Bar" that has "Foo" as it's _show-category_. I would expect my WordPress app to look like this:  www.mysite.com/shows/foo/ =&gt; shows all posts under the foo category www.mysite.com/shows/foo/bar =&gt; shows the indivual post   I try to avoid plugins when possible, but am open to any solution. So I have learned in class that light can get red-shifted as it travels through space. As I understand it, space itself expands and stretches out the wavelength of the light. This results in the light having a lower frequency which equates to lowering its energy.  My question is, where does the energy of the light go? Energy must go somewhere!   Does the energy the light had before go into the mechanism that's expanding the space? I'm imagining that light is being stretched out when its being red-shifted. So would this mean that the energy is still there and that it is just spread out over more space? Many people want to try/use Android without buying a new Android phone.  How can I install Android on my current phone or device running Nokia Symbian, Maemo, or MeeGo; Microsoft Windows Mobile or Windows Phone 7/8/10; Apple iOS (iPhone); RIM's BlackBerry OS; Palm's WebOS; Samsung's Bada; HP's WebOS; Mozilla's Firefox OS; or other phone / operating system? After using the simple LM317 on breadboard variable power supply for a while, a need for a more rugged and reliable bench power supply has arose.    Short on money, i decided to build it as many other amateurs like me did. The thing is that, for my current needs i don't need a giant digitally controlled multi-channel 500 watt beast or something like that.  Instead what i really want is a low wattage positive and negative low voltage ouput -12v-0v-12v for example. However i really like that my power supply to be safe, reliable and fool-proof as far as possible. So after searching the web here and there, i found many designs that from my point of view fell in one of two divisions:-   Ones that use discrete op-amps and transistors. And ones that use integrated voltage regulators.   So -at least for me- i think that the ones with discrete op-amps and transistors are more prone to malfunctions and issues compared to the integrated ones with all of their internal over current and thermal protection circuits which would need to be discretely implemented in the bench power supplies that utilize discrete op-amps, however those designs have the advantage of ease of customization and more importantly that it is easier to have 0V output compared to 1.2V in integrated voltage regulator ones.    So i like advice to help me choose between circuits that utilize discrete op-amps like this circuit for example:-  Or ones that use integrated voltage regulators with their intrinsic robustness and low form factor.    Also as a side but related question i have seen many designs on the web that utilize negative voltage fed to the adjust or like pins to achieve 0V output from integrated voltage regulators like this single positive power supply:-     Or a positive and negative channels power supply that i really like its design because of simplicity (not because of laziness but to avoid the drawbacks that may come with complex designs especially when implemented by an amateur like me):- And the question is      Is it wrong or a system safety and reliability lowering act to feed negative voltage to adjust pin for LM317 for example?     I ask this question because the datasheet clearly states that the working output range is 1.2V-37V for LM317 for example, also no similar circuit is mentioned in the Typical Applications section except for the following one:- And even in that circuit, however the adjust pin is tied to the negative rail, it does't regulate during this interval instead it is shut until the next half wave at least that what i understand.    So at last to sum it up which alternative is best suited for my needs, its pros and cons and suggested circuits if possible. I believe that umask is something that controls , but do not fully understand it.  After running umask 0644 in a , I cannot read the files I create with the command-line text editor nano. I noticed that the permissions of that file are set to 0022 instead of the default 0755.  How does umask work? I thought I could just remove the each digit in the umask from 0777, 7 - 6 = 1 and 7 - 4 = 3, so I expect the permissions to be 0133, but apparently, this is not the case.   What is umask exactly? Explain it to me like I was a "Linux noob" How do I calculate with umask? What are use cases for umask? Why is 24.0000 not equal to 24.0000 in MATLAB? I am writing a program where I need to delete duplicate points stored in a matrix. The problem is that when it comes to check whether those points are in the matrix, MATLAB can't recognize them in the matrix although they exist.  In the following code, intersections function gets the intersection points:  [points(:,1), points(:,2)] = intersections(...     obj.modifiedVGVertices(1,:), obj.modifiedVGVertices(2,:), ...     [vertex1(1) vertex2(1)], [vertex1(2) vertex2(2)]);   The result:  &gt;&gt; points points =    12.0000   15.0000    33.0000   24.0000    33.0000   24.0000  &gt;&gt; vertex1 vertex1 =     12     15  &gt;&gt; vertex2     vertex2 =     33     24   Two points (vertex1 and vertex2) should be eliminated from the result. It should be done by the below commands:  points = points((points(:,1) ~= vertex1(1)) | (points(:,2) ~= vertex1(2)), :); points = points((points(:,1) ~= vertex2(1)) | (points(:,2) ~= vertex2(2)), :);   After doing that, we have this unexpected outcome:  &gt;&gt; points points =    33.0000   24.0000   The outcome should be an empty matrix. As you can see, the first (or second?) pair of [33.0000 24.0000] has been eliminated, but not the second one.  Then I checked these two expressions:  &gt;&gt; points(1) ~= vertex2(1) ans =      0 &gt;&gt; points(2) ~= vertex2(2) ans =      1   % &lt;-- It means 24.0000 is not equal to 24.0000?   What is the problem?    More surprisingly, I made a new script that has only these commands:  points = [12.0000   15.0000           33.0000   24.0000           33.0000   24.0000];  vertex1 = [12 ;  15]; vertex2 = [33 ;  24];  points = points((points(:,1) ~= vertex1(1)) | (points(:,2) ~= vertex1(2)), :); points = points((points(:,1) ~= vertex2(1)) | (points(:,2) ~= vertex2(2)), :);   The result as expected:  &gt;&gt; points points =      Empty matrix: 0-by-2 I am trying to calculate the final velocities of two equal mass 2-dimensional circles after an elastic collision. I have tried to figure it out using formulas I know from high school physics, but nothing seems to work. My known variables are:   initial x and y velocities for each circle x and y distances between the centres of the circles at the time of the collision   The variables I would like to solve for are:   final x and y velocities for each circle   Here are diagrams showing all the variables: The spell Armor of Agathys states:      You gain 5 temporary hit points for the duration. If a creature hits you with a melee attack while you have these hit points, the creature takes 5 cold damage.   Now, assume my buddy uses Inspiring Leader to give me 10 temporary hit points — does the effect end? How do I get permissions to delete files on Windows 7? I updated my laptop's OS from Windows XP to Windows 7. There are some leftover files from Windows XP on the computer now. If I try deleting them I get the following error:     You need permission to perform this action.      You require permission from S-1-.... to make changes to this folder.   What's weird is that I am logged in with the only user account on this machine and I have administrator privileges. I tried turning UAC off, but I still can't delete the files.  How can I force removal of these files? What should I look for when shopping for my first DSLR? I am thinking of buying a digital SLR camera. What things should I be looking for? I've got a problem while unwrapping UVs. When I'm unwrapping UVs it showing me this message.     Why is this happening?