How to get the value of a textbox using jQuery?
How do I get the value of a textbox using jQuery?
Let $a_1=1$ and $a_n=n(a_{n-1}+1)$ for $n=2,3,\dots$. Define $$P_n=\left(1+\frac{1}{a_1}\right)\left(1+\frac{1}{a_2}\right)\dots\left(1+\frac{1}{a_n}\right)$$Find $$\lim_{n \to \infty}P_n$$   Trial: $$1+\frac{1}{a_n}=1+\frac{1}{n(a_{n-1}+1)}\;.$$ But I can't simplyfy.Please help. For a simple circuit with a battery supplying a voltage $V$ to a capacitor, let us assume that the charge on the capacitor is $Q$. Now, the work done by the battery or the energy supplied is given by the relation:  $$W=QV$$  But the energy stored in the capacitor is given by:  $$U = \tfrac12 QV$$  The value of $Q$ as well as that of $V$ should be the same in both the equations.  Now my question is, where is the other half of the energy that the battery supplied? What is the name of this castle part? Why don't my female dwellers give birth to children? Is there an Attribute I can use in my class to tell DataGridView not to create a column for it when bound to a List Real Analysis, Folland Problem 1.3.15 Measures Given a measure $\mu$ on $(X,M)$, define $\mu_0$ on $M$ by $$\mu_0(E) = \sup\{\mu(F): F\subset E \ \text{and} \ \mu(F) &lt; \infty\}$$ a.) $\mu_0$ is a semifinite measure. It is called the semifinite part of $\mu$. b.) If $\mu$ is semifinite, then $\mu = \mu_0$ (Use Exercise 14) c.) There is a measure $\nu$ on $M$ (in general, not unique) which assumes only the values of $0$ and $\infty$ such that $\mu = \mu_0 + \nu$.  The proof of Exercise 14 can be found  For a.) I believe we need to show that $\mu_0(E) = \infty$. Perhaps we can do this by proof of contradiction, similarly to what the proof in the link above does (actually it seems identical). For b.) I am not sure how we can show $\mu = \mu_0$ I think maybe we have to show by construction that $\mu \leq \mu_0$ and $\mu \geq \mu_0$ For c.) I haven't any idea for. Any suggestions is greatly appreciated. Double-column listing package Not too well up on LaTeX, but I want to use the listings package for listings spanning a two-column format.  Unfortunately, asterisks cannot save me (like for figures/tables); this doesn't work:  \begin{lstlisting*} ... \end{lstlisting*}   I've Googled about, but got no satisfactory answer, and getting a bit desperate. Should be simple... hope I'm not missing something stupid. Perhaps it's possible to embed this into a separate spanning float?  Help?  (P.S., I've posted this on the main stackoverflow site as well...  if this is considered a duplicate, please comment and I'll remove the other. Getting a bit desperate fighting a deadline.) Why the name 'Rogue One'? So far, is there any suggestion, or speculation as to the reason for the name 'Rogue One' for the next Star Wars film?   To me, the name seems very close to the Rogue Squadron, most known from Hoth (their leader Luke Skywalker), especially the number following Rogue like a callsign.   However as far as I know, they were formed after the first Death Star destruction. So why Rogue One? Print file content without the first and last lines Is there a simple way I can echo a file, skipping the first and last lines? I was looking at piping from head into tail, but for those it seems like I would have to know the total lines from the outset. I was also looking at split, but I don't see a way to do it with that either. Why is this trigger finding a null value despite the field being populated? Financial Account is a child of Client in a Master-Detail relationship. The client (John Sandbox) has a Wealth Advisor, 'John Smith', on his client record, however, the system debug that pulls finAcct.client__r.Wealth_Advisor__c shows this field as 'null'.  Does anyone have any idea why I am not getting the value in this field? The goal of this trigger is to make sure that the lookup fields for the Client Team (one of which is 'Wealth Advisor') always match between the client record and the financial account record when they are linked. Thanks!      Boolean UpdateMe;     List &lt;Financial_Account__c&gt; FinAcctsToUpdate = new List&lt;Financial_Account__c&gt;();      //Loop through all Financial Accounts in Trigger.new     for(Financial_Account__c finAcct : newFinAccts){         UpdateMe = false;          System.debug('finAcct WA Lookup: ' + finAcct.Wealth_Advisor_Lookup__c);         System.debug('Client: ' + finAcct.client__c);         System.debug('Acct WA: ' + finAcct.client__r.Wealth_Advisor__c);          if (finAcct.Wealth_Advisor_Lookup__c != finAcct.client__r.Wealth_Advisor__c){             finAcct.Wealth_Advisor_Lookup__c = finAcct.client__r.Wealth_Advisor__c;             UpdateMe = true;         }         if(UpdateMe == true){             FinAcctsToUpdate.add(finAcct);         }         UpdateMe = false;     }      if(FinAcctsToUpdate.size() &gt; 0 ){         update FinAcctsToUpdate;     } Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$. In the book Principles of Physics by Resnick Halliday: The decrease in Potential energy of a parallel plate capacitor due to a dielectric is because the slab would start to oscillate and the energy would transfer back and forth between the kinetic energy of the moving slab and potential energy stored in the electric field. First of, can somebody provide me the math of the SHM and could somebody explain why it would become the potential of the capacitor i.e. the electric field and not the potential of the slab? As the slab is doing SHM, shouldn't the slab(and not the capacitor) have potential energy at one point of time and kinetic at another like a spring? If the SHM is because of the electric field due to the conducting plates in capacitors, won't they always be in one direction (Plus, it's magnitude is not even a function of distance!)? Could someone be kind enough to provide the math and the reason for Potential and Kinetic Energy transfer question? How to copy some, but not all files? how to write in TeX "computer zero" with slanted vertical line on it? In TeX, how is computing zero sign written with slanted vertical line on it? If integral is zero and function is continuous and non negative, then what about the function? Divisibility by 7 rule, and Congruence Arithmetic Laws Let $L$ and $R$ be $n \times n$ matrices. I am trying to solve the following minimization problem  $$ L^{k+1} := \arg \min_{L} \lambda \|L\|_{\ast} + \frac{1}{2\mu}\|L-R^{k}\|_{F}^{2} $$ $$ \mbox{s.t.}\ L \succeq 0 $$  where $\|\cdot\|_{\ast}$ and $\|\cdot\|_{F}$ denote the nuclear and Frobenius norms, respectively. Also, $k$ expresses the $k$th iteration when solving an optimization problem successively.  I don't know how to solve this problem. Would you tell me the way? How can I pay tolls on Japanese expressways? I'm renting a car soon in Japan and am planning to travel on the expressways. What's the best way to pay tolls? What's the thing with $\sqrt{-1} = i$? Do they really teach this in the US? It makes very little sense, because $-i$ is also a square root of $-1$, and the choice of which root to label as $i$ is arbitrary. So saying $\sqrt{-1} = i$ is plainly false!  So why do people say $\sqrt{-1} = i$? Is this how it's taught in the US? Migrate to *any* site?