Value of $5050\cdot\int^1_0(1-x^{50})^{100} dx/\int^1_0(1-x^{50})^{101} dx$
Find the ratio of $\frac{\int_{0}^{1} \left(1-x^{50}\right)^{100} dx}{\int_{0}^{1} \left(1-x^{50}\right)^{101} dx}$
How accessible are the Stack Exchange sites for users of screen reader software? There are some plans to put more information on  which is a Stack Exchange site. I am concerned it may not be as readable to everyone as it could be on a plain wiki.  Is there any information on how to use Stack Exchange with a screen reader? Enable Careers and Jobs in app Vertical line for the the right margin in Notepad++ What is the best way to determine the number of days in a month with JavaScript? I've been using this function but I'd like to know what's the most efficient and accurate way to get it.  function daysInMonth(iMonth, iYear) {    return 32 - new Date(iYear, iMonth, 32).getDate(); } How do R and Python complement each other in data science? In many tutorials or manuals the narrative seems to imply that R and python coexist as complementary components of the analysis process. To my untrained eye, however, it seems that both languages sort of do the same thing.  So my question is if there are really specialized niches for the two languages or if it's just a personal preference whether to use one or the other? I'm married have a job with stable income.I have 2 kids. I have applied for UK visit visa about 7 years ago and was refused. I can't remember what exactly was the reason for refusal.  I want to travel for tourism to spend 9 days and my budget is around 1300GBP for the trip. I would be spending part of my annual leave in the UK. I have the following people in UK: Mother, Dad, Sister(she's married), Brother (married), Uncle and Aunt.  I'm travelling alone since my wife is pregnant. I haven't travelled since I was in school then.  I will be on my yearly 21 days annual leave during which I will be spending 9days in UK. I can't think of anything more about my circumstance.  So what should a cover letter look like?  secondly I have just 1 account where my salary is paid in monthly and my savings.I will be submitting the 6 months bank statement for the account.  Additional question:  In the income &amp; expenditure where one is asked to indicate if I have income and savings,should I click Yes or No. And if Yes should state the ending balance as at the time of my application. Is there a systematic way of finding the conjugacy class and centralizer of an element? Could the task be simplified if we are working with "special groups" such as $S_n$ or $A_n$? Are there any intuitive approaches? Thanks. How can I deduce/identify an app from a notification icon? Asking users to accept answer when they comment that it answers their question I've had a couple of answers today where the OP indicated via a comment that I solved their problem, but the question wasn't upvoted or accepted.  In both cases the person probably wasn't able to upvote since they were new, but they could have accepted my answer. I felt a little guilty asking them to accept the answer, but since it solved their problem I felt that it would help others who stumbled on the question trying to solve their own problem to know that my solution really was the answer. Is asking the OP to accept your answer when they've said that it solved their problem a reasonable thing to do or does that feel like nagging for reputation? How can you prove that the normal equations: $(X^TX)\beta = X^TY$ have one or more solutions without the assumption that X is invertible?  My only guess is that it has something to do with generalized inverse, but I am totally lost. Detecting Mouse clicks in windows using python Let $A_n$ denote an $n \times n$ tridiagonal matrix.  $$A_n=\begin{pmatrix}2 &amp; -1 &amp; &amp; &amp; 0 \\ -1 &amp; 2 &amp; -1 &amp; &amp; \\ &amp; \ddots &amp; \ddots &amp; \ddots &amp; \\ &amp; &amp; -1 &amp; 2 &amp; -1 \\ 0 &amp; &amp; &amp; -1 &amp; 2 \end{pmatrix} \quad\text{for }n \ge 2$$  Set $D_n = \det(A_n)$  Prove that $D_n = 2D_{n-1} - D_{n-2}$ for $n \ge 4$. Least-action classical electrodynamics without potentials Is it possible to formulate classical electrodynamics (in the sense of deriving Maxwell's equations) from a least-action principle, without the use of potentials? That is, is there a lagrangian which depends only on the electric and magnetic fields and which will have Maxwell's equations as its Euler-Lagrange equations? What does the "Alternative Character Sheet" mean when it asks you for the "Maximum Hit Dice" and the "Remaining Hit Dice"? I am trying to fill in the "Alternative Character Sheet" (one of the ). It asks me for my "Maximum Hit Dice" and the "Remaining Hit Dice". What do these terms mean? Algorithm to match one input file with given numbers of file Error-Handling in Swift-Language Trying to Remember a Book that explored evolution of Dinosaurs to intelligence and then encountering humans Many, many years ago, I read a book where dinosaurs were assumed to have suvived the K-T event (or it never happened), and they evolved to intelligent species that used not only language (which combined sound, posture, and colour changes on their skin) but also used technology.  In the series, a human is captured or somehow gets integrated with one of the evolved dinosaur groups.  Again, from a very faint memory, the dinosaurs had a level of technology that would be about middle ages, and the humans were much more analogous to American Indian.  That's really all I can recall about the book, and I am trying to find it for my daughter to read.  Can anyone help me out? Creating Users on secondary server in log shipping I have a production Server say ServerA I have setup log shipping to ServerB which is left in read-only mode. The purpose of this log shipping is to lower the load on production server for some expensive queries (painful reports).   Now if I have to create some logins using our domain accounts. I cannot do this because the secondary database is in standby mode.   I thought if I create these logins on Primary server it will be copied over to secondary server then the logs are restored there but this isnt the case.   I have done a lot of research online finding a way around to this. I found the following resources for this. I tried every method suggested in this articles but none of them seems to work.   1)   2)   3)   Has someone experienced the same issue? what did you do? Is there any way around for this issue? Any suggestions any pointer please. Is the reason why the time evolution operator is unitary based on purely physical arguments, i.e. that the physical processes that an isolated system undergoes shouldn't depend on any particular instant in time (homogeneity of time); thus two experimenters who conduct the same experiment starting from the same initial state, but at different times, should have the same probability amplitude for that state?! Or is there some mathematical argument as well?  Also, is the reason why the time evolution operator is linear implied by the superposition principle (as an arbitrary state can be expressed as a linear combination of basis states the operator should act linearly as otherwise the state as a whole would evolve differently to the superposition of states that it was initially represented by)?! Numlock turned on on boot-up I have a desktop running ubuntu 10.04  I want numlock to be turned on initially.  What do I have to change to accomplish this?  ~~edit~~  I checked in my BIOS.  It was already set up to have the numlock turned on initially.  Yet it isn't being turned on initially.  I have a USB keyboard: would that break this functionality?   Or, should I ask elsewhere (superuser, perhaps) about how to get that BOIS setting working properly?