bypass activation lock on i pod touch 5th generation
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Default Class Accessibility in C# by default is a class:   private ? internal ?  sealed ? Algebric proof for the identity $n(n-1)2^{n-2}=\sum_{k=1}^n {k(k-1) {n \choose k}}$ Prove the identity:  $$n(n-1)2^{n-2}=\sum_{k=1}^n {k(k-1) {n \choose k}}$$  I tried using the binomial coefficients identity $2^n = \sum_{k=1}^n {n \choose k}$  but got stuck along the way. $ \lim_{x\to o} \frac{(1+x)^{\frac1x}-e+\frac{ex}{2}}{ex^2} $ $$ \lim_{x\to o} \frac{(1+x)^{\frac1x}-e+\frac{ex}{2}}{ex^2} $$   (can this be duplicate? I think not) I tried it using many methods  $1.$ Solve this conventionally taking $1^\infty$ form in no luck  $2.$ Did this, expand $ {(1+x)^{\frac1x}}$ using binomial theorem got $\frac13$ then grouped coefficients of $x^0$ and it cancelled with $e$ then took coefficient of $x$ cancelled with $\frac{ex}{2}$ and so on   very messy right ? at last I got $\frac13$ but that's not the expected answer!  I must have went wrong somewhere can anyone help me with this. Does separation of variables in PDEs give a general solution? When a partial differential equation is solved using the separation of variables method, is the produced solution the most general one that satisfies the equation or have we lost some forms of the solution because of the assumption that it is in the form of separated variables? Significance of starting the Fibonacci sequence with 0, 1.... DISCLAIMER: I do not deal with in-depth mathematics on a daily basis as some of you may, so please pardon my ignorance or lack of coherence on this topic.  QUESTION: What is the significance of starting the Fibonacci sequence with $0,1$ ?  For instance, if I picked any two random integers, say 2 and 7, to start a sequence would I actually be creating some multiple or derivation of the Fibonacci sequence?  Is there a general mathematical explanation for the relationship between any sequence represented by $a[0] = x, a[1] = y, a[n] = a[n-1] + a[n-2]$ and the Fibonacci sequence?  Or, back to my example sequence, is there a general mathematical relationship between:  $2,7,9,16,25,41,66,107,173,280...$  and  $0,1,1,2,3,5,8,13,21,34...$  Perhaps the Golden Ratio explains it somehow?  Any help would be appreciated. For $x$ and $\lambda$ complex, if $|x| \gt \frac{1}{2} + \sqrt{\frac{5}{4} + |\lambda|}$ then $|x^2+\lambda| \gt |x| +1$ What is the difference between "Redirection" and "Pipe"? This question may sound a bit stupid, but I can not really see the difference between redirection and pipes.  Redirection is used to redirect the stdout/stdin/stderr, e.g. ls &gt; log.txt.  Pipes are used to give the output of a command as input to another command, e.g. ls | grep file.txt.  But why are there two operators for the same thing?  Why not just write ls &gt; grep to pass the output through, isn't this just a kind of redirection also? What I am missing? Harry: "He made seven Horcruxes?"   Dumbledore: "...Not seven Horcruxes: six. The seventh part of his soul, however maimed, resides inside his regenerated body..." (HP6, US Hardback, page 503).    I would think that Dumbledore had already known that there were 6 horcruxes:    the diary  Gaunt's ring  Salazar's locket Helga Hufflepuff's cup Nagini (the whole essence divided thing)   Now those are the five that he was sure of. He knew that when Riddle came to Hogwarts to ask for the DADA position, he was really there so he could hide a horcrux. (But he never got a chance to tell Harry that, right?) Did Dumbledore know of the diadem? Or did he just think Riddle wanted to hide the cup?   Did Dumbledore say there were 6 and not 7 because he didn't know about the diadem but did know about Harry being a horcrux? Or did he say there were 6 to ensure Harry didn't guess he was a horcrux? Sorry if this makes no sense.  I know that in the end there were 7 horcruxes and an 8th part of Voldemort's soul right? How do I write a correct micro-benchmark in Java? This book came out of the 1970s (early 1980's) at the latest. In it the protagonist, a not so diligent student, gets turned on to computer programming and creates (I think..) a weather program.   Eventually he moves on and years later the program contacts him. It has become an AI and he is its creator.  I forget what the setup is post contact which is not helpful at all.. join comma delimited data column Given a countable collection of metric spaces $\{(X_n,\rho_n)\}_{n=1}^{\infty}$.  Form the Cartesian Product of these sets $X=\displaystyle\prod_{n=1}^{\infty}X_n$, and define $\rho:X\times X\rightarrow\mathbb{R}$ by  $$\rho(x,y)=\displaystyle\sum_{n=1}^{\infty}\frac{\rho_n(x_n,y_n)}{2^n[1+\rho_n(x_n,y_n)]}.$$  Show that $\rho$ is a metric on $X$ whose induced topology is equivalent to the product topology on $X$.  So basically what this problem is saying is that there's a canonical way to define a metric on the countable product of metric spaces.  I showed in a previous problem that the topology induced by $\rho_n$ is equivalent to that induced by $\frac{\rho_n(x_n,y_n)}{1+\rho_n(x_n,y_n)}$.  And thus we can go ahead and just assume that $\rho_n&lt; 1$ for all $n$ and replace our infinite series by  $$\rho(x,y)=\displaystyle\sum_{n=1}^{\infty}\frac{\rho_n(x_n,y_n)}{2^n}.$$  Now comes the interesting part: how should I go about showing that the product topology on $X$ and the topology induced by $\rho$ are equivalent?    The basis for the product topology given to me in my book's definition is that of cartesian products made up the $X_n$ except for finitely many which are $O_n$ for some open subset of $X_n$.  However I believe I was able to improve upon this and show that I could decompose these into a basis where the $O_n$ were all open balls induced by their respect $\rho_n$ metric.  For $\rho$ I'm using the basis of open balls that it induces, as I can see no other reasonable choice.    However I can't seem to match these two bases up.  There are many different points $\{x_n\}\in X$ which make my infinite series less than a certain value and there is so much freedom in which terms in the series I choose to reduce in size that it seems hopeless to try and fit an open ball induced by $\rho$ into any one of my basis elements for the product topology.    Is there a more appropriate strategy for proving these two topologies are equivalent? Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$? CSS z-index causes part of tags to show through notifications on webmasters, web applications, gaming, gamedev, and their meta sites When you vote 35 times in a day and you only have five votes left, you start getting a warning popup that you are almost at your limit.  When this warning appears in the same place as the tags, part of the tags shows through it.        This screen shot was taken on webmasters.    This is also a problem on Web Applications: :        and :        This also happens on  as described .  Here is a .  It is also happening on the meta sites associated with the sites that have the problem.   For example, here is web apps meta site:    This a minor annoyance that has been around for at least a couple years. I currently have Windows 7 on my computer and I want to install Ubuntu alongside Windows safely.  Could someone please provide clear instructions? How do I bypass restrictions on the length of the PATH variable System Properties      This environment variable is too large. This dialog allows setting values up to 2047 characters long.   I use/have used a lot of software, and my PATH has grown as a result. When I try to add new paths, I get the above message. As a workaround, I'm editing my user path, but prefer not to. After my online research on the subject, I learnt that, biologically speaking, many scientists believe that there is no such thing as a race. Homo sapiens as a species is only 200,000 years old, which has not allowed for any significant genetic diversification yet, and our DNA is 99.99% similar. I've read statements that there can be more genetic variation inside a racial group than between different racial groups, meaning that, for example, two individuals from the same "race" can have less in common with each other than with an individual from another "race".  :     Scientists consider biological essentialism obsolete, and generally discourage racial explanations for collective differentiation in both physical and behavioral traits     Q1: If Homo sapiens has no races (according to biologists), why are we so different morphologically? (hair/eyes/skin colour and even athletic performance seem to differ between human populations)  Q2: Is it common for other species too, when genetically close populations have very different morphological traits? Are there any other mammal or animal species that exhibit biological diversity comparable to human diversity, and how do taxonomists treat these species? (excluding intentionally bred domestic species to keep the comparison fair)    The question has been paraphrased to emphasize that it is the biological debate that is in question, not the sociopolitical. I.e., why is there no consensus in evidence and opinions of scientists? Inheriting non-implicit constructors on Apex classes If I have an abstract parent class like this:  abstract class Vehicle {     public Vehicle(Person driver) {         //     } }   and then I create a child class like this:  public class MagicCarpet extends Vehicle {     //this won't compile }   I encounter the following Compile Error:     Error: Parent class has no 0-argument constructor for implicit construction at line ... column ...   Obviously I can explicitly re-declare a constructor on the child class toget it to compile:  public class MagicCarpet extends Vehicle {     public MagicCarpet(Person driver) {         super(driver);     } }   But I feel this isn't DRY. Not sure what's actually going on under the covers here.  How can I get a constructor (other than the implicit 0-argument one) to be inherited by a child class? How does a Windows 10 'digital license' activate the OS? In cricket how does someone become an umpire at international level? Is there some procedure for this? How are they selected and what is the criteria for this?