Chrome standalone for linux (no root)
How can I install a package without root access?
So my teacher gave a pretty tough (for me) problem in class today: Does the series $$ \sum_{n=1}^{\infty}\frac {\sin{\frac 1 n}} {\sqrt n} $$ converge or diverge?  So far I've thought of trying the Comparison Test and Ratio Test but couldn't really get anywhere. Intuitively I think it should converge, but how do I actually show this? What's the process to change a site logo? Who is responsible for defining a site logo? I mean, there are moderators of the site that define it, or stackexchange defines it? I am trying to count the number of bit-strings of length 8 with 3 consecutive zeros or 4 consecutive ones. I was able to calculate it, but I am overcounting. The correct answer is $147$, I got $148$.  I calculated it as follows:  Number of strings with 3 consecutive zeros = $2^5+5\times2^4 = 112$, because the 3 zeros can start at bit number 1, 2, 3, .., 6  Number of strings with 4 consecutive ones = $2^4+4\times2^3 = 48$, I used the same reasoning.  Now I am trying to count the number of bit-strings that contain both 3 consecutive zeros and 4 consecutive 1s. I reasoned as follows:   the strings can be of the following forms: 0001111x, 000x1111, x0001111..thus there are $2+2+2 = 6$ possibilities for bit-strings where the 3 consecutive zeros come first. Symmetrically there are $6$ bit-strings where the 4 consecutive ones come first.  Thus the answer should be = $112+48-12 = 148$.  clearly there's something wrong with my reasoning, if someone could point it out, that would be awesome. Thanks Usage of __slots__? What is the purpose of  in Python — especially with respect to when I would want to use it, and when not? How to cancel a jquery.load()? Can a familiar attune and wear or use a magic item? Is it possible for a familiar to attune to and then wear or wield a magic item? How to count the node a user has created in a View? Path.Combine for URLs? is handy, but is there a similar function in the .NET framework for ?  I'm looking for syntax like this:  Url.Combine("http://MyUrl.com/", "/Images/Image.jpg")   which would return:  "http://MyUrl.com/Images/Image.jpg" Can a Muggle inadvertently create a horcrux-like object? I think that we have it well-established (regardless of whether or not one sees this as flawed logic) that Harry is not a Horcrux.  A Horcrux has to be made intentionally, and the recipient is cursed and classified as an "evil object," etc.  Neither of which is true for Harry - so, as stated by JKR herself, Harry is not a Horcrux as such.  But the fact remains that murder can, in fact, accidentally create something that shares a key property of the Horcrux: the soul splits, attaches itself to the nearest recipient, and lingers inside.  As it does in Harry's case.  So my question is: is this only true for wizards?  A Muggle cannot utilize a spell to create a Horcrux.  But, if a Horcrux-like object / being can be created accidentally through murder without intentional Horcrux-creating spells, can this also happen in the case of a Muggle committing murder?    Can a Muggle commit murder, have their soul split, and have the piece of the soul inadvertently attach itself to something nearby without any Horcrux-creating spell being cast? I started reading "The Mathematics of nonlinear Programming - AL peressini" recently.  Theorem : Suppose that $f(x) , f'(x) ,f''(x)$ exist on the closed interval $[a,b]$. If $x^* ,x $ are two different points of $[a,b]$ , then there exists a point $z$ strictly between $x^*$ and $x$ such that   $$f(x)=f(x^*)+f'(x^*)(x-x^*)+\frac{f''(z)}{2}(x-x^*)^2$$  I tried to prove this theorem using The Fundamental theorem of calculus. But I can not stop it at the second derivative . Do I have to use mean value theorem ? or is there a simple proof for this ? Looking for the name of a post apocalyptic/sci-fi tv show or film Every once in a while this starts nagging me, I have really no idea and not much to go on so here goes...  A man wearing a blue? uniform walks into a town that looks abandoned and empty and all covered in dust.  The skies are brown/dirty with no sun.  He goes into the upstairs of one of the houses. He stops at I think a fireplace, examines something, or it’s like he’s remembering something.  Then downstairs in the street, a man/person wearing rags/robes with bandages covering his face starts banging on a fire hydrant with a stick/pipe. More people in bandages/robes start appearing, there's a chase in the town. I don't remember much but he's chased into wastes? through a gully or ditch and then a vehicle (only really remember that it was steel in colour) shows up and a woman comes and shoots one or two of the people chasing him.   That’s about all I remember. I was about 6 or 7 maybe and it was afternoon maybe a little later.  I thought maybe Star Trek, but after searching I don't think it is. I think it might be 80's, maybe early 90's. I think it's sci-fi rather than post-apocalyptic. Why didn't the Seons change? In the book Elantris, the Reod was caused by a giant earthquake opening a chasm which changed the shape of all the Aons. The Seons, which are basically living Aons, were presumably unchanged, since nobody noticed the change, which should have been obvious on the simpler Aons. In how many different ways can we place $8$ identical rooks on a chess board so that no two of them attack each other? In how many different ways can we place $8$ identical rooks on a chess board so that no two of them attack each other?  I tried to draw diagrams onto a $8\times8$ square but I'm only getting $16$ ways.  Does that sound right?  Thanks for the help! How to show this function's discontinuity?  $ f(n) = \left\{     \begin{array}{l l}      \frac{xy}{x^2+y^2} &amp; \quad , \quad(x,y)\neq(0,0)\\      0 &amp; \quad , \quad(x,y)=(0,0)    \end{array} \right.$ Cartesian products and families I have some trouble trying to understand Halmos' explanations about generalized Cartesian products. I've read these entries already:    This also has the page I'm stuck on.      Is his generalization the same as a Cartesian product of several sets? As here:   What puzzles me is $\{a,b\}$. Where does it come from, what does it do? I know that it is supposed to be arbitrary. How does it identify distinct elements of $X \times Y$? Does some function map each $a \in A$ to an element in $X$? Or is it always the same $a$?  What does he mean by      the set $Z$ of all families $z$, indexed by $\{a,b\}$, such that $z_a \in X$  and $z_b \in Y$   ? What does does an element of $Z$, namely one family $z$, consist of? By family, does he mean an indexing function or the indexed elements? This comes to a very important question for me: Does family mean a function or the set of all indexed elements?   I will try to explain how I understand it thus far: $Z$ contains elements of the form $\{(a,x),(b,y)\}$. The choice of $x$ depends on $a$, so an $x$ in a $z \in Z$ equals the $z_a$ of $X$. Now, we want to map these pairs to $X \times Y$, so we have a function $f$ that takes $z \in Z$ and connects it to the corresponding ordered pair $(z_a, z_b)$, where $z_a \in X$. $X \times Y$ is not the same as $Z$; they only, effectively, contain equal elements.  He goes on:     If $\{X_i\}$ is a family of sets ($i \in I$), the Cartesian product of the family is, by definition, the set of all families $\{x_i\}$ with $x_i \in X_i$ for each $i$ in $I$.   How I understand it: $\{X_i\}$ contains, as elements, several sets, each single one a set $X$ identified by an index/element of $I$. Then, we go over all indeces $i$ in $I$, take from each set $X$, namely $X_i$, an element $x$ and add it to current set of the newly created sets/families. So, the lower index $i$ does not refer to an element of $X_i$ indexed by $i$, but rather calls all elements of $X_i$ $x_i$. We end up with a set, defined as Cartesian product, of sets, in which each element (set) contains ordered elements, each from a different $X_i$. How does the ordering occur?  $\prod_i X_i$, the Cartesian product, becomes equal to $X^I$, if all $X_i$ are the same set $X$. $X^I$ means all possible combinations of mapping from $I$ to $X$. We randomly take an elements $x$ from some $X_i$, put it in a set/family with other randomly obtained $x$, put the entire set into a set denoted $X^I$, and continue doing so, till we have no more options. Then, each set in the new $X^I$ contains a mapping of some $i$ to some $x$. Since we exhausted the options, they are indeed all combinations.  Where did I go wrong? Someone needs to spoonfeed my the answer; I am completely confused by now. What is the difference between 32-bit and 64-bit Ubuntu? I've heard the 64-bit platform performs better and can detect more than 4GB of RAM. Also, while some apps haven't ported to 64-bit yet, ia32-libs lets a 64-bit machine run them.  If so, why not promote 64-bit over 32-bit? How can I always run the command prompt as administrator? Travel without an Italian residence permit in the Schengen area 74190 counter problem So, I got my 74190 counter shows number like this  9-8-7-6-5-4-3-2-1-0-5-4-3-2-1-0-5-4-3-2-1-0-5-4-3-2-1-0 and so on.  My questions:   What can I do to change the output count down into 5-4-3-2-1-0-5-4-3-2-1-0 and so on? When it changes 0 into 5 it moves so fast. How could I fix this one? How can i make the grass bend when this cube hits it?  Here's the picture: