is there a way to execute a function when I have its name in a string
How to execute a JavaScript function when I have its name as a string
This problem occurred to me when I came across a similar problem where the radii were taken over only the primes. That question was unanswered, but it seems to me infinitely many circles of radius $1/2, 1/3, 1/4...$ can fit into a unit disk. The area of all those circles would be $\pi \sum_2^\infty 1/n^2 = \pi^3/6 -\pi$, which is less than the area of the unit disk $\pi$. But can the circles actually be packed with no overlaps? Best approach to Windows Forms rolling log output in TextBox I get the following error when i do sudo apt-get update  W: GPG error: http://ppa.launchpad.net precise Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 6AF0E940624A220   I tried following ways after reading various questions here and also by googling.  I tried  sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 6AF0E1940624A220   It did not help. I also tried  sudo gpg --keyserver hkp://keyserver.ubuntu.com:80 --recv-keys   thinking port 11371(default) may be blocked due to firewall.  I also tried to reset everything as follows  sudo rm /var/lib/apt/lists/* -vf sudo apt-get update &amp;&amp; sudo apt-get upgrade   still i get the same error or get update. Any other possible solution I can try? Playing a remote movie on the remote computer How to replace the_post_thumbnail template tag and show the first inside the post image instead How to find $\sum_{r\ge 0} \binom{n}{r}\binom{n-r}{r} 2^{n-2r}$? Problem was to find $$\sum_{r\ge 0} \binom{n}{r}\binom{n-r}{r} 2^{n-2r}.$$ My partial progress i tried to motivate such that upper term in binomial terms gets constant rather than variable , so i thought of changing it to form $\binom{n}{n-r}\binom{n-r}{n-2r}$. Now it's of the form $\binom{n}{m}\binom{m}{k}$. We know it is equivalent to $\binom{n}{k}\binom{n-k}{m-k}$. Doing this we get $\binom{n}{2r}\binom{2r}{r}2^{n-2r}$. Now what I need to do as next step as such still nothing the upper or lower terms r any constant values(sum to ) , all are variables still. Now by one answer by Robpratt i got by snake oil , is there any other way to solve this problem ? Is it a problem if a UK visa was issued but not used? Last year, my wife and I were issused 6-month visieor visas for the UK. She did not travel with me and, therefore, didn't use her visa. I am currently applying for a visitor visa for my daughter and myself.  Will the fact that my didn't use her visa have any negative affect on our new application? What makes Stealing Signs wrong? The Matching Problem/Derangements - n letters to n people There are n letters addressed to n eople at different addresses. The n addresses are typed on n envelopes.  A disgruntled secretary shuffles the letters and puts them in the envelopes in random order, one letter per envelope.  Find the probability that at least one letter is put in a correctly addressed envelope. [Hint: use the inclusion-exclusion formula.] What is the probability approximately, for large n ?    My attempt at a solution:  P(all correct) = $\frac{1}{n!}$  P(n-1 correct) = ${n \choose n-1} \frac{1}{n!} = \frac{1}{1!(n-1)!}$  ${n \choose n-1}$ ways of selecting n-1 correct letters.  P(n-2 correct) = ${n \choose n-2} \frac{1}{n!} = \frac{1}{2!(n-2)!}$  ...  P(n-n correct) = ${n \choose n-n} \frac{1}{n!} = \frac{1}{n!(n-n)!} = \frac{1}{n!}$  This all looks ok to me, but I tested this for a case of 4 people, (I think the theoretical value should be $\frac{9}{24}$ but obviously that is not what I got. Can someone correct my logic please? Also, with regards to the hint about inclusion/exclusion - where would that come in?  I read about derangements on Wikipedia but it did not make total sense to me (the derivation).  I would appreciate any advice whatsoever including references to other material. Short brandable domain vs. long keyword domain Variable amount recurring billing Hi i'm looking for a payment gateway that can do recurring billing that changes month to month.  Fogbugz do this, they charge based on how many active users there were that month. All of the APIs that i've found only let you set a fixed amount and it's difficult/impossible to vary the subscription amount month to month.  Has anyone come across any services that do this? Why does the question's closed status disappear when clicking to load a new edit? Canonical vs. non-canonical terminal input Do AWS Reserved Instances need to be assigned to the instance? I have an RDS instance running of type db.t2.small.  I bought a reserved instance for 1 year of the same type, I paid the partial upfront rate.  Do I need to assign this subscription in some way to my existing instance to say 'This is the instance that is using the subscription' or does AWS just charge for the instance usage depending which instances you have running and whether an available subscription was active for it at the time which determines the running rate?  The reason that I ask is that I can't see any mention of the reduced rate on my AWS Billing area and it shows that I've used 17 hours of my reservation, but there isn't a row on my bill so far this month that indicates the new partial upfront rate that I should be charged for my instance. "Install Spotify" can't be opened because Apple cannot check it for malicious software I'm running macOS 10.15 Catalina Beta.  When I try to install Spotify I see the following error:    Is this a Spotify issue or a Catalina issue?  Thanks. Minimum bounty on a question is now 100 rep? Prove that $ n < 2^{n}$ for all natural numbers $n$. Prove that  $ n &lt; 2^{n}  $ for all natural numbers $n$.  I tried this with induction: Inequality clearly holds when $n=1$. Supposing that when $n=k$, $k&lt;2^{k}$. Considering $k+1 &lt;2^{k}+1$, but where do I go from here?  Any other methods maybe? How can I increase the mouse pointer speed beyond the limits set by the Mouse preferences dialog? In the Mouse preferences dialog I've set the acceleration to max and the sensitivity to min and the mouse pointer is not exactly sluggish, but I'd like to make it even faster. Is it possible to be done by setting some value in the procfs or something?  Thanks! Clipboard.GetText returns null (empty string) My clipboard is populated with text, but when I run  string clipboardData = Clipboard.GetText(System.Windows.Forms.TextDataFormat.Text);   I get back an empty string. I've toyed with various forms of the call including:  string clipboardData = Clipboard.GetText(); string clipboardData = Clipboard.GetText(System.Windows.Forms.TextDataFormat.UnicodeText);   But with the same result.  Am I missing something obvious? Programmatically disable apt unattended upgrades How can I programmatically/script disable apt unattended upgrades? Running Ubuntu 16.04.