Is it appropriate to ask for more than one recommendation letter from the same person
How frequently can you ask for a personal reference without being disrespectful?
Regex matches but shouldn't How can I model flips until N successes? You and I decide to play a game where we take turns flipping a coin. The first player to flip 10 heads in total wins the game. Naturally, there is an argument about who should go first.  Simulations of this game show that the player to flips first wins 6% more than the player who flips second (the first player wins approx 53% of the time).  I'm interested in modelling this analytically.  This isn't a binomial random variable, as there are no fixed number of trials (flip until someone gets 10 heads). How can I model this?  Is it the negative binomial distribution?    So as to be able to recreate my results, here is my python code:  import numpy as np from numba import jit   @jit def sim(N):      P1_wins = 0     P2_wins = 0      for i in range(N):          P1_heads = 0         P2_heads = 0         while True:              P1_heads += np.random.randint(0,2)              if P1_heads == 10:                 P1_wins+=1                 break              P2_heads+= np.random.randint(0,2)             if P2_heads==10:                 P2_wins+=1                 break     return P1_wins/N, P2_wins/N   a,b = sim(1000000) Prove that $(a+1)(a+2)...(a+b)$ is divisible by $b!$ The problem is following, prove that:  $$(a+1)(a+2)...(a+b)\text{ is divisible by } b!\text{ for every positive integer a,b}$$    I've tried solving this problem using mathematical induction, but I don't think that i did it correctly. Here's what i've done  $1.\ b=1\ (Basis)$  $$b!| (a+1)(a+2)...(a+b)$$ $$1 | a+1 \text{, which is true}$$  $2.\ b=k\ (Induction\ Hypothesis)$  $$k! | (a+1)(a+2)...(a+k)\text{, we assume it's true}$$ $$k!*n = (a+1)(a+2)...(a+k)\text{, n is some positive integer}$$  $3.\ b=k+1\ (Inductive\ Step)$  In order to prove I should get:  $$(k+1)!*m = (a+1)(a+2)...(a+k)(a+k+1)\text{, where m is some positive integer}$$ $$(a+1)(a+2)...(a+k)(a+k+1) = k!*n*(a+k+1)$$ $$(a+1)(a+2)...(a+k)(a+k+1) = (k+1)!*n + k!*n*a$$ $$(a+1)(a+2)...(a+k)(a+k+1) - a(a+1)(a+2)...(a+k) = (k+1)!*n$$ $$(a+1)(a+2)...(a+k)(k+1) = (k+1)!*n$$  And as you can see I'm returning at the beginning.  Also I've tried to use the fact that in b consecutive numbers, there must be at least one that divides b, but since i eliminate that number (because I couldn't be sure that the quotient is divisible with (b-1) or (b-2) or ... or 2. And after this i can't continue with (b-1) using this method, because it's not necessary for the other (b-1) to be consecutive. Regular (non-moderator) users should be able to override deletions by Community user There is a question on  that got deleted by the Community user. This question isn't terrible (we have worse one's there), and I'm not complaining about this question in particular.  I wanted to vote to undelete it. However, it says "A moderator has deleted this post and it cannot be undeleted". This "moderator" is Community!  I understand if a "real" live human moderator (no offense to all non-humans out here) deleted this question that we can't override it. But this is a Robot! It sees that it got a downvote, no answer and little activity for a while and just deletes it.  Can we have "Community user" have rights to delete, but have those "deletions" subject to normal-person override? How do I iterate over a range of numbers in Bash when the range is given by a variable?  I know I can do this (called "sequence expression" in the Bash ):   for i in {1..5}; do echo $i; done   Which gives:     1    2    3    4    5   Yet, how can I replace either of the range endpoints with a variable? This doesn't work:  END=5 for i in {1..$END}; do echo $i; done   Which prints:     {1..5} Proof verification: Set of partial limits of a sequence is closed Algorithm for computing Hadamard product of two rational generating functions If I have two generating functions $A(x) = \sum_na_nx^n$ and $B(x) = \sum_n b_nx^n$   then the Hadamard product is $(A \star B)(x) = \sum_{n} a_nb_nx^n$.  Now when $A$ and $B$ are both rational functions ($P(x)/Q(x)$ with polynomials $P, Q$) I've seen non-constructive proofs that $A \star B$ is also rational.  Given two rational generating functions $A$, $B$, is there an algorithm that efficiently computes $A \star B$? Or at least a constructive proof you could use to write an algorithm? Is char *envp[] as a third argument to main() portable Recursivly Deleted Root Directory I recursively deleted the contents of my root directory with sudo privileges. My display reset, and windowing stopped working. I could no longer run non-buitin commands. Most of my directories (including the home directory disappeared).  What I meant to run:  sudo rm ./* -rf   What I believe I ran:  sudo rm /* -rf   I understand how this command works (see ).  I'm trying to get a better sense of how much (and what parts) of the original files and directory-structure physically remains on the hard-drive.  How much of these "remains" are recoverable? E.g is it possible to use data recovery software like TestDisk/PhotoRec to recover the full home dir itself? What about config files? Allow bounty to be set with reputation from another site? What is the correct way to completely remove an application? I've searched the net for such information and found different command lines, like these ones:  sudo apt-get remove application sudo apt-get remove application*  sudo apt-get remove --purge application sudo apt-get remove --purge application*  sudo apt-get purge application sudo apt-get purge application*   So, what is the correct way? Is it necessary to use that "*"?  After that, I also found these commands:  sudo updatedb sudo locate application sudo rm -rf (file/folder name) To prove the convergence of the p-series   $$\sum_{n=1}^{\infty} \frac1{n^p}$$  for $p &gt; 1$, one typically appeals to either the Integral Test or the Cauchy Condensation Test.  I am wondering if there is a self-contained proof that this series converges which does not rely on either test.    I suspect that any proof would have to use the ideas behind one of these two tests. Using residue theorem to integrate from $-\infty$ to $\infty$ I'm trying to integrate $$\int_{-\infty}^{\infty} {x^2 \over {(x^2 + 1)}^2(x^2 + 2x + 2)} $$ given that the function  $$f(z) = {z^2 \over {(z^2 + 1)}^2(z^2+2z+2)} $$ has residues $${9i - 12 \over 100},{3 - 4i \over 25}$$ at the poles $i$ and $-1+i$ respectively. From my understanding of this I have added the two residues (by the residue theorem, and because their respective poles lie in the upper half plane) and multiplied by $2\pi i$ and got an answer of $14\pi \over 100$  Have I done this right? Why could the pictures and paintings in Hogwarts talk and the photos of Harry's parents couldn't? Website is under maintenance - how to restrict access? When my phone MOTOROLA G3(2015) is updated to Marshmallow, its not showing files when connected to PC. While connecting, it shows options as charing only, PTP, MTP, MIDI. When I select MTP, it shows the external card, but not showing the contents, where as internal memory is detected and all files are shown. I have two hard drives. One is used for Windows and one is empty. I want to install Ubuntu on the empty hard drive. The Windows hard drive is disk0 in Windows and the empty hard drive is disk1. When I install Ubuntu and it asks where I want to install it, I choose "Something Else" but I am stuck there. What do I choose for "boot loader installation"? How can animals in the wizarding world go close to extinction? Change all @username references in comments when a user changes their name? The fact that a user can change their name at will can lead to some confusion in the comments.  For instance, suppose a user named "foo" changes his name to "bar", all those comments signed by "foo" are now signed by "bar", but responses to "bar"'s comments still start with "@foo".  Could those "@foo" references in comments be changed to "@bar"?    A brief discussion on this has set me straight.  I didn't think it through.  Request withdrawn. There are some kind of door devices which push the door back after we open the door and come out.  My problem is that the door area is not constructed in a way that such a device can be installed.  There is no space adjacent to the door anywhere.  Automatic closure of door is extremely important to me.   Please see following pictures and tell what choices do I have.