Proof of divergence of $1/2 + 1/3 + 1/5 + 1/7 + 1/11 +....$
Does the sum of reciprocals of primes converge?
Straight lines - product of slope of perpendicular lines. Let $l$ be a line with slope $\frac{1}{0}$, and $m$ a line with slope $0$.  Now, line $l$ is perpendicular to line $l$, therefore the product of the slope of line $l$ and the slope of line $m$ equals $-1$. This implies that $\frac{1}{0} \times 0 = -1$! A $60\times 60$ board is partitioned into rectangles of size $2\times 5$ (or $5\times 2$). Is it true that there always exist another partition into rectangles of size $1\times 3$ (or $3\times 1$) such that any $2\times 5$ (or $5\times 2$) rectangle contains a $1\times 3$ (or $3\times 1)$ rectangle?  For the "simple" partition into $2\times 5$ rectangles, this is certainly true: use the simple partition into $1\times 3$ rectangle.  Another way to partition is to first partition the $60\times 60$ board into $12\times 10$ boards, and then for each such board, put two $2\times 5$ at the top and ten $5\times 2$ below. It is not hard to tile each such $12\times 10$ board with $1\times 3$ (or $3\times 1)$ rectangles so that each $2\times 5$ (or $5\times 2$) contains a $1\times 3$ (or $3\times 1)$ rectangle.  (I'm assuming that an $m\times n$ rectangle has $m$ rows and $n$ columns.) C# Structs: Unassigned local variable? Is it OK to crosspost Stack Overflow questions, now that the Portuguese SO is open? How can install Desktop Toggl on Ubuntu 13.04? I try type:  sudo add-apt-repository ppa:official-toggl/ppa sudo apt-get update sudo apt-get install desktop-Toggl    But getting information desktop-Toggl not found. Combinatorics, choosing 3 elements from 100 In how many ways can we pick three different numbers out of the group $1,2,3,\dots,100$ such that the largest number is larger than the product of the two smaller ones? (The order in which we pick the numbers does not matter.) I am using the document class article. Once I place a part in the document, all subsequent sections belong to the part automatically. How can I reset a section such that it does not belong to a part?  The following sample demonstrates what I want to achieve:  \section{Introduction}  \part{Part 1} \section{Section 1 belonging to part 1} \section{Section 2 belonging to part 1}  \part{Part 2} \section{Section 1 belonging to part 2} \section{Section 2 belonging to part 2}  % should not belong to Part 2 \section{Conclusion} How to get GUI sudo password prompt without command line? Currently, for all my commands that require root access, I have to type them out on a command line.  I would like for the GUI to prompt me to key in my password, when sudo is required, instead of having to type out the commands from command line.  Is there any way to enable this? Previously one version of Ubuntu desktop had this feature out of the box.  This version of Ubuntu (that I am now running) I upgraded from a server installation.  I will add, my user account is already added to sudo group. Thus I can run commands such as sudo gedit or sudo apt-get but I'm not able to install software in the Ubuntu Software Center. How do you sort du output by size? Async Await Handler Deadlock Showing that $e^x > 1+x$ How to search for questions and answers between two users? I am searching for the questions posted by me (user:139150) that were answered by another user.    His ID is: 55159    There does not seem to be any way to search for posts where both the users are involved. I wanted to switch to Xfce (I had KDE and GNOME installed), and I did this :    sudo apt-get install xubuntu-desktop sudo apt-get remove kubuntu-desktop sudo apt-get remove ubuntu-desktop sudo apt-get autoremove   but to my surprise, I could still pick gnome, kde plasma, etc during the log in.  So, how do I completely remove KDE and GNOME desktops? Standard nomenclature for component types What prefixes should be used on reference designators for components of various types?  I think we can all agree that "R##" refers to a resistor, "C##" refers to a capacitor, and "L##" refers to an inductor.  Beyond that, it appears to be a mishmash of conventions.    I've seen both "IC" and "U" used for chips.   "Q", "T", and "M" have been used for transistors and MOSFETs.  Ordinarily, "D##" is used for diodes, but LEDs and Zeners get special treatment on some boards.    What standards are available for reference, and who endorses them?  JEDEC, ISO, IEEE, and other standardization bodies are welcome references (though I'd prefer an inexpensive standard), but I'm also curious to see what's used at various companies other than my own.    Edit:  What I'd really like to see is a list in an answer here which complies with the standard (even if it's just a quote). Sed -- Replace first k instances of a word in the file I want to replace only the first k instances of a word.  How can I do this?  Eg. Say file foo.txt contains 100 instances occurrences of word 'linux' .  I need to replace first 50 occurrences only. grouped bar chart with pgfplots Configure Postfix to use external MX servers for delivery of local mail if user is unknown How to handle fragmentation of auto_increment ID column in MySQL Combinatorial proof of $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$. Windows vs Linux Local Time?