I just want to make the image in the frame move with every frame of the video.
I have a video clip of a car driving by from left to right. My goal is to add a decal (mask) to the car door.  Right now I am painstakingly moving the mask via X and Y.
The series $\sum_{n=2}^{\infty }\frac{1}{\log (n!)}$ I'm trying to find out whether this Series $\sum_{n=2}^{\infty } a_{n}$ converges or not when $$a_{n}=\frac{1}{\log (n!)}$$  I tried couple of methods, among them: d'Alembert $\frac{a_{n+1}}{a_{n}}$,   Cauchy condensation test $\sum_{n=2}^{\infty } 2^{n}a_{2^n}$, and they both didn't work for me.  Edit: I can't use stirling, and integral.  Thank you I would like to remove selected commit log entries from a linear commit tree, so that the entries do not show in the commit log.  My commit tree looks something like:  R--A--B--C--D--E--HEAD   I would like to remove the B and C entries so that they do not show in the commit log, but changes from A to D should be preserved. Maybe by introducing a single commit, so that B and C become BC and the tree looks like.  R--A--BC--D--E--HEAD   Or, ideally, after A comes D directly. D' representing changes from A to B, B to C and C to D.  R--A--D'--E--HEAD   Is this possible? if yes, how?  This is a fairly new project so has no branches as of now, hence no merges as well. My Prof wrote that   $\sum_{n=2}^{\infty} n(n-1)x^{(n-2)} = \frac{2}{(1-x)^3}$  when $-1&lt; x&lt;1$  I do not understand where the above formula comes from. Can someone please explain the steps or provide a hint?   Thanks! A number of questions "has been" or "have been" asked? Formally, is it correct to write:     A number of questions has been asked here.   or:     A number of questions have been asked here.   As a non-native speaker of English, I would prefer the former: the subject seems to be "number", therefore the verb ought to be singular, I'd say. However, the latter seems more common, and therefore I believe that my gut feeling is just plain wrong — but I would really like to have a definite answer.  Moreover, is it the same for "a myriad of", "a plethora of", and so on? Add the font changes as options in our preferences Why can't variables be declared in a switch statement? Where are Upstart log messages on Ubuntu 13.X? Why has the innkeeper put a price on my head? So, I was just assaulted by a trio of fairly well armed thugs while walking out of Riften. Before attacking me, they informed me that they were 'here to teach me a lesson.'  After dispatching them in due course, I found this on the body of what I can only assume to be the leader, given his vastly superior armaments:   Orgnar is the innkeeper in Riverwood. Now, I admit, I've stolen a fair amount, but I pride myself on having never been caught. My total bounty to date is at zero. So, how did he figure out that I stole something, why is he taking the law into his own hands, and if I go back to Riverwood, am I going to get shanked? Microsoft.Office.Interop.Excel doesn't work on 64 bit How to add some non-standard font to a website? Is there a way to add some custom font on a website without using images,  or some other graphics?  For example, I was working on a wedding website, and I found a lot of nice fonts for that subject. But I can't find the right way to add that font on the server. And how do I include that font with CSS into the HTML? Is this possible to do without graphics? How to pause with specific time between two command in script? I want to do such as following:  #!/bin/bash command1 pause 30 seconds command2 exit   This is only example script with pause of 30 seconds between run of 2 command.  How to do this? Should a "thank you" comment, for instance Thanks for your answer, be flagged as non-constructive?  If a "thank you" comment is flagged as non-constructive what would the moderator reaction to this flag be? Would it be marked as helpful, or not? Time dependent Schrödinger equation with time independent potential and separation of variables suppose we have a potential that's independent of time $V(x,t) = V(x)$ so in Schrödinger equation we get: $$i\hbar \frac{\partial \Psi (x,t)}{\partial t}=-\frac{\hbar^2}{2m}\frac{\partial^2 \Psi (x,t)}{\partial x^2}+V(x)\Psi(x,t)$$ since the LHS involves a variation of $\Psi$ with $x$ and the LHS involves a variation of $\Psi$ with $t$ can we say that a basis for the solutions will be with the form $\Psi(x,t)=\psi(x)T(t)$? $f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$ Question is to prove :  $f : S^1 \to \mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$  I guess it would be helpful to use intermediate value theorem  Assuming $f(x)\neq f(-x)$ then given any $p\in (f(-x),f(x))$ (assuming $f(-x)&lt;f(x)$) there exists $y\in (-x, x)$ such that $f(y)=p$  I am not very sure of how to use this..   It would be helpful if someone can give some hint which would help me to solve this..  Thank you. In English, the number 0 is treated as plural. It is then:   0 seconds 1 second    1.2 seconds   2 seconds     Shouldn't it be "nobody want to go there," instead of "nobody wants to go there"?  I also saw in TOEFL that "any __" should be used with a singular.  But I see it very common that it is a plural also.  Why is that?  (updated: example, "we don't have any apples any more" vs "If you get any apple, please let me know.") The infinite product of the sines of all positive integers is zero I tried to prove that $\prod\limits_{k = 1}^\infty  {\sin k = 0}$  Define $$P(m)=\prod\limits_{k = 1}^m  {\left|\sin k\right|}$$  then I take the logarithm of both sides $$\log P(m)=\log \prod\limits_{k = 1}^m  {\left|\sin k\right|}$$  which can be written as $$a_m=\log P(m)=\sum\limits_{k = 1}^m  {\log\,\left|\sin k\right|}$$ for any $k\in\mathbb{N}$ we have $0&lt;\left|\sin k\right|&lt;1$, so all terms of the sum above is strictly negative.  I say that the sequence diverges: $\left\{a_m\right\}_{m\in\mathbb{N}}\to\,-\infty$  This is a delicate point on which I have some doubts.  I know that  $$\int\limits_0^\pi  {\log \left|\sin x\right|{\text{ d}}x}  =  - \pi \log 2$$ and that the function $\log \left|\sin x\right|$ is periodic with period $\pi$,  so the integral from 1 to $\infty$ diverges to $- \infty$. Then the series diverges as well for the integral test for convergence.  As $\log P(m)\to\, -\infty$ we can say that $P(m)\to\,0$ as $m\to\,\infty$  Therefore $$\mathop {\lim }\limits_{m \to \infty } \prod\limits_{k = 1}^m {\left| {\sin k} \right| = \mathop {\lim }\limits_{m \to \infty } \prod\limits_{k = 1}^m {\sin k = \prod\limits_{k = 1}^\infty  {\sin k = } 0} }.\quad \blacksquare$$ To ensure that a new chapter starts on a right-hand page, the book class (and the report class with the options twoside and openright) will insert blank pages between chapters if necessary. However, these pages still contain the headers and footers as defined by the class. How can I remove those?  Note: I know that I can manually add \clearpage\thispagestyle{empty} at the appropriate points of my document. However, this seems awkward and is prone to fail if I change my document later. I'm looking for automatic solutions. Pointer to class data member "::*" I came across this strange code snippet which compiles fine:  class Car {     public:     int speed; };  int main() {     int Car::*pSpeed = &amp;Car::speed;     return 0; }   Why does C++ have this pointer to a non-static data member of a class? What is the use of this strange pointer in real code? In CSS what is the difference between "." and "#" when declaring a set of styles? What is the difference between # and . when declaring a set of styles for an element and what are the semantics that come into play when deciding which one to use? Don't show pending suggested edits to me after I run out of votes