Infinite sum of a series $\frac{N}{100} .( \frac{99}{100})^{(N-1)}$
How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
Any way to add CSS for a single page/node? I'm cleaning up my big crazy style sheets (possibly pertinent to a future question) and I'm wondering the best way to add custom CSS to a specific node or page. In particular, my work site's home page is a Panel Page and it has a bunch of different styling. Right now the CSS is just included with the main theme style sheet. Is there a way to say, &quot;if this is node Foo, then add foo.css&quot;? Is  what I'm looking for? I might be interested in generalizing this to other nodes/sections/etc, but at the moment I just want to handle this one item. I'm attempting to make an elevation profile from a DEM in ArcMap using the Interpolate Line tool.  I've done this before, and it has worked great--basically I just draw a line with Interpolate Line, then click Profile Graph to get the elevation profile.  However, for some reason, it's not working now: when I draw out my line, nothing shows up on the map.  I don't get a line, and I can't figure out what I'm doing wrong.  I've searched online for an answer, but to no avail.    Any tips? Verify that $4(29!)+5!$ is divisible by $31$. I know that like is a preposition but why not using it as conjunction?  Examples:        It's as if I'm walking on air   It's like I'm walking on air      What is the difference? Is a general GRE score of X sufficient for entry to postgraduate degree Y? Question: I got general GRE scores of VR (verbal reasoning), QR (quantitative reasoning), and AW (analytical writing).  Is this a good score to apply for entry to postgraduate degree in field X?  How will this score look to the selection committee?    Note: This is an intentionally generic GRE question (with unspecified scores and field of study) which is intended as a template for a large number of questions asked on this forum regarding evaluating the scores on the general GRE test (e.g., , , , , , , , and ).  This question seeks answers that are applicable for an applicant for graduate-level programs in any field, based on any scores in the GRE general test.  The goal of this question is to provide a general reference to avoid the need for specific questions with particular scores/field of study. Replace all occurrence of character except first one How to relate areas of circle, square, rectangle and triangle if they have same perimeter?? I was given a question which was like:     Suppose that a circle, square, rectangle and triangle have same perimeter. How area their areas related??   My work:  I broke the question in parts and tried to prove it seperately:  STEP $1$. Suppose the given perimeter is $P$.So the radius of circle will be ${r=P/2\pi}$.  And hence area of the circle will be:   ${P^2/4\pi}$.  Side of square will be $P/4$ and hence area of square will be $P^2/16$.   It is obvious that ${P^2/4\pi}$  >  $P^2/16$.   So Area of circle is more than area of square.  STEP $2$: Whether by using $AM&gt;GM$ inequality or by using a bit of differentiation, we can get that product off two quantities is maximum when they are equal.  So, Area of square is more than Area of rectangle.  Here, the hardest part come (at least for me). I can't relate the area of triangle to any of Circle, Square or Rectangle. It would have been easy if the triangle was Equilateral, Right angle but the question is talking about a general triangle.  However, when I considered the situation with different examples (Assuming the perimeter and calculating the area, I got the relation:  Circle > Square > Rectangle > Triangle.  I shall be highly thankful if you guys can establish the relation in purely mathematical way.  EDIT: This question does not ask that whether circle have the largest area among all 2-D figures or not. The OP just want to relate the areas of Circle, Square, Rectangle, Triangle in a pure mathematical way. Where to place my local website starting with the 2.4.7 version of apache2? I recently installed Ubuntu 14.04, then I installed lamp-server and placed my webpages in /var/www directory, but when I opened localhost in the browser there was nothing. I think that happened because Zend updated Apache.  Whatever the reason may be, I want to know where to keep my php files so that I can access them from my browser. Using url package without hyperref makes link hit boxes erratic I've currently got a url link in a footnote in my document. With the hyperref package, everything works correctly. Because the IEEE PDF Express tool doesn't like having the hyperref package, I've removed it and only left in the url package.  However, some strange behavior occurs as a result of this. Instead of just the link being clickable, entire paragraphs of text before/after end up being clickable and going to the same link. This occurs for both Skim and Preview in Mac OSX.  Does anyone have an inkling of what might be causing this? Show that antipodal points remain antipodal under any isometry of $S^2$ "The antipodal map of $S^2$ is the isometry $\bar m$ sending each point $P$ to its opposite point $-P$" (from textbook)  Show that antipodal points remain antipodal under any isometry of $S^2$. In other words, for each isometry f of $S^2$, if $P$ and $P'$ are antipodal, then so are $f(P)$ and $f(P')$  I am unsure how I can define the $P$ and $P'$ so that they are opposites of each other in the antipodal map, and am I supposed to apply the traditional isometries (translation, reflection and rotation) to the points? I don't understand this problem. Polynomial rings in infinitely indeterminants How can we prove that (the set of all polynomials in infinitely non commutative indeterminants over $k$) is a ring, where $k$ is a ring with unity?   Adding two polynomials is a polynomial, but for commutativity  How can we show the following: $ax_1+bx_2=bx_2+ax_1$ (commutativity of addition) If we have finite number of variable it is easy to prove it, (we take the $n-1$ variables...), but what about the infinite number of variables?  Can someone give me a hint? How to highlight important parts (with a gray background) In the below link        the author highlights anything which is important using a greyish color background. For example, if you see Equation 1.5.3 (which on page 22 of the book) it is highlighted in grey. I would like to know the TeX commands for producing similar output. Combining values in one column (or part) when values in another column (or part) match I was wondering what is the purpose of piping the downloaded file by curl into sudo -E bash - in the following shell:   curl -sL https://deb.nodesource.com/setup_5.x | sudo -E bash - One word for things that would be nice to have, but not required to have? If I see an answer that involves some illegal activity, such as breaking license agreements, should I then mark this as Offensive or should I simply down-vote it? So all wizards get an invitation to Hogwarts at 11... How do they know whom to invite?  If a wizard is Muggle-born, then nobody would know about their existence.  Or do they register some weird magical stuff being done by them before 11? Should I vote to close a duplicate question, even though it's much newer, and has more up to date answers? From the Cracks in time and space story arc it's known that if a TARDIS is blown up (possibly while in the Time Vortex) it rips creation itself apart. Also, from the Stolen Earth / Journey's End we learn the Daleks' masterplan which is subjugating creation itself via destroying it with the Reality Bomb (unfading Z-neutrino energy radiation).  In the Last Great Time War all sorts of temporal weapons were used and it's known that Daleks have the ability of time travel as well. Why didn't they use the Time Vortex back then to win the war once and for all via detonating a TARDIS while inside? Who should I be damage buffing as Mercy