I need to calculate the sum of this series.   $\sum_{n=2}^{\infty}\frac{1}{n(n^2-1)} $  By using the partial fraction, I obtained this sum: $\sum_{n=2}^{\infty}-\frac{1}{n}+\frac{1}{2(n+1)}+\frac{1}{2(n-1)} $  Proceeding in the replacement of incremental values of n I noticed that some element is simplified, but I can not get a useful form to calculate the sum. any help?
As my question says,   $$\frac 1{1.2.3}+\frac 1{2.3.4}+\frac 1{3.4.5}+...$$  As far as $\frac 1{1.2}+\frac 1{2.3}+\frac 1{3.4}+...$ is concerned, we can write it as $\frac 1{n-1} - \frac 1{n}$ What can we do here?
Adding a Method to an Existing Object Instance I've read that it is possible to add a method to an existing object (i.e., not in the class definition) in Python.   I understand that it's not always good to do so. But how might one do this? I'm writing my final report in LaTeX for my bachelor's degree. I'm aiming at having a document similar to the .doc template used normally.   I want to have my customs headers and footers applied on pages when I'm starting a new chapter.  I'm using documentclass report with fancyhdr and lastpage packages.  My headers are defined like this:  \lhead{\myTitle} \rhead{\today} \cfoot{\thepage\ of \pageref{LastPage}}   My chapters are created using standard \chapter{title} macro.  On pages with new chapters, the only headers/footers I see is the standard page number at the bottom.  What should I do?  EDIT: I've finally gone with Peter Breitfeld's solution. I'Ve gone a step further and created my own chapter command:  \newcommand{\myChapter}[1]{     \chapter{#1}     \thispagestyle{fancy} }   Thanks for the help! input to pic with 12V and resistors I have 12V, Use these 12V to power a device (that has a 12V output signal) and to power a 7805. After the 7805 there is a pic microcontroller where I would have to connect the output from my device. I was thinking of having 2 resistors in a 3/1 ratio in order to have about 4V at the pin of the pic. Can this be done, given that the ground is common, or will it give some sort of problem with the lm7805? How can I mass rename files? I've got a bunch of files named with a the pattern 99 - DescriptiveName.txt and I'd like to remove the number from the front so I just have DescriptiveName.txt.  How can I do this? Can I do it from the command line or is there a utility that can do this? Node.js on multi-core machines Undergraduate research field different from PhD field I am a Physics undergrad who is interested in pursuing a PhD in pure maths in the future (algebraic geometry/topology) but I am a bit unsure. My question is quite general, and I don't wish to provide more background for fear of bias in the answers.  My question: Is it is advisable/possible/unfavorable/favorable to apply for a PhD in a field, different from that in which you have done most of your undergraduate research?  My research (includes just reading and understanding papers, writing summaries until now, I havent published anything) mostly includes Quantum field theory, and gauge theory. Would the selection committee turn down an application to a pure maths field, if I have no research experience whatsoever?  I would also like to ask the question other way round. What if I concentrate my undergraduate research SOLELY on topics in pure maths such as algebraic geometry/topology and take other physics courses, would I be able to apply to a string theory PhD with a high chance of success?  Should I consider spending time on both of these (which is almost an impossible task), to improve my chances in both the areas or would research in one area, and grad level courses in the other suffice?  In brief: Should the PhD field you are applying to be the same as your undergraduate research area? I have a bunch of SD cards that do not have the little plastic switch for the read only setting. so Windows thinks it’s write protected or something. The card is not write protected by the software lock present on the SD card standard.  I’m using one with tape over the notch and it’s ugly. Also, the Thinkpad slot drags on the tape all the time so I’m afraid it will might loose in there eventually.  So, is there any way to tell Windows to ignore this lame write-protect feature?  I’m not interested on the SD card itself as it’s irrelevant for the issue at hand. Read this question as being about a 5.25” floppy disk drive instead of an SD card if you wish. I’m pretty sure the Windows settings are the same for both, really.  I’m  that there are 3 ways to secure an SD card. I’m talking about only the mechanical switch, which is the responsibility of the host to handle. How do I detect what .NET Framework versions and service packs are installed? A similar question was asked , but it was specific to .NET 3.5. Specifically, I'm looking for the following:   What is the correct way to determine which .NET Framework versions and service packs are installed? Is there a list of registry keys that can be used? Are there any dependencies between Framework versions? I'm a beginner at photography and own a Canon 20D with two lens; a 50mm prime and a 17mm-85mm zoom.  I've purchases all my filters at 67mm to fit my zoom lens and use a  to use them with my prime lens.  I'm looking at buying a . My question is, will the same principal work? Can I buy a 67mm wide angle lens and use it on my 52mm prime without any trouble.  One of the reasons for the purchase of a wide angle is my cropped sensor makes the 50mm prime rather close - I'm hoping the wide angle will make it easier to capture more.  Many thanks for any help in advance. Pete Why non-measurable sets exist? What Is the reason behind the fact that $\Bbb R$ is not a complete measure space? Is it only due to the cardinality of  $\Bbb R$? Or other structures on  $\Bbb R$ also play a role? Can one make every subset of  $\Bbb R$ trivially measurable by assigning them to a number of a complete ordered field of the cardinality $\aleph_2$ ? Universal Chord Theorem How to decide whether missing values are MAR, MCAR, or MNAR I have a large proteomics dataset. In the rows I have the proteins , and in the rows I have the samples.The dataset contains a lot of missing values.  I would like to know I can find out whether missing values are MAR, MCAR, or MNAR, and how I can decide the best imputation technique. Kind regards. Due to my ignorance, I find that most of the references for mathematical analysis (real analysis or advanced calculus) I have read do not talk much about the "multivariate calculus". After dealing with the single variable calculus theoretically, it usually directly goes to the topic of measure theory.    After reading the wiki article "", I'd like to find the rigorous proof for this test. The first book comes to my mind is Courant's Introduction to Calculus and Analysis which includes the multivariate case in the second volume.   Motivated by this, I'd like to put the question here:     What are the usual references for the   theoretical treatment for   ? How to get the type of T from a member of a generic class or method Let's say I have a generic member in a class or method, like so: public class Foo&lt;T&gt; {     public List&lt;T&gt; Bar { get; set; }          public void Baz()     {         // get type of T     }    }  When I instantiate the class, the T becomes MyTypeObject1, so the class has a generic list property: List&lt;MyTypeObject1&gt;. The same applies to a generic method in a non-generic class: public class Foo {     public void Bar&lt;T&gt;()     {         var baz = new List&lt;T&gt;();                  // get type of T     } }  I would like to know what type of objects the list of my class contains. So what type of T does the list property called Bar or the local variable baz contain? I cannot do Bar[0].GetType(), because the list might contain zero elements. How can I do it? no cycles if and only if has $n-m$ connected components Interactive / Real time code compilation for stackoverflow.com. That will improve the answer correctness of the stackoverflow.com.  When adding a new code block, let the user try to compile the code and see the result. It will be useful to demonstrate class designs, algorithms, and logics. Can you enter UK later than intended date of travel on the visa application? Direct proof that nilpotent matrix has zero trace I'm just starting to learn linear algebra and I understand Gaussion elimination but I don't understand this proof:    Is the heart of this the fact that all the while when I've been row-reducing matrices to reduced row-echelon form... I've actually been multiplying a matrix by a series of a elementary matrices?  What does the notation $[A\ \ 0]$ mean?  How is the equation $A = E_1^{-1}...E_k^{-1}$ arrived at? Just for curiosity, sometimes while installing software throught apt-get install software_name the terminal prompt me for a confirmation "type Yes or No", but not allways.  I dont mean the sudo password prompt, but the message "Will be downloaded and configrated XXX Kb, continue?" (or something similar)  Why?