Where did the Programmers Stack Exchange site go?
Is "Software Engineering" the replacement of "Programmers"?
Testing convergence of series $\sum_{n=3}^\infty\frac{1}{n (\ln(n))^p(\ln\ln(n))^q}$ Lets have this problem. $$\sum_{n=3}^\infty\frac{1}{n (\ln(n))^p(\ln\ln(n))^q}$$ I have rewritten this to a form $$\sum\frac{1}{np'^{\ln\ln(n)}q'^{\ln\ln\ln(n)}}$$ For $p,q\in\mathbb{R}$. Obviously, $p',q'&gt;0, p=\ln(p'),q=\ln(q')$ Prove that if the positve term series $\sum^{\infty}_{n=1}a_n$ is convergent, also $\sum^{\infty}_{n=1}\sqrt{a_na_{n+1}}$ is convergent.  Prove that if the positive term series $\sum^{\infty}_{n=1}a_n$ and $\sum^{\infty}_{n=1}b_n$ are convergent, also $\sum^{\infty}_{n=1}a_nb_n$ is convergent.  I've tried to solve it using comparison test, but no results. How can infinite information be theoretically encoded or stored in a single qubit? I've just gotten started with Nielsen and Chuang's text, and I'm a little stuck. They mention that theoretically, it would be possible to store an infinite amount of information in the state of a single qubit. I'm not sure I completely comprehend this.    Here's how I rationalized it: You take all the information you want to store, put it in binary form, and make it the real component of $\alpha $ or $\beta$ (the coefficients of the computational basis states).   Now I'm not sure if I've understood it right, but since it's still fuzzy in my head it would be great to get some kind of ELI5 explanation or possibly a more detailed picture of how this would, even theoretically, be possible.    Apologies if the question doesn't meet standards. I'm new to the forum and would be open to feedback regarding asking questions or answering them. How can I do case insensitive string comparison in Python?  I would like to encapsulate comparison of a regular strings to a repository string using in a very simple and Pythonic way. I also would like to have ability to look up values in a dict hashed by strings using regular python strings. Deriving even odd function expressions What is the logic/thinking process behind deriving an expression for even and odd functions in terms of $f(x)$ and $f(-x)$?  I've been pondering about it for a few hours now, and I'm still not sure how one proceeds from the properties of even and odd functions to derive: $$\begin{align*} E(x) &amp;= \frac{f(x) + f(-x)}{2}\\ O(x) &amp;= \frac{f(x) - f(-x)}{2} \end{align*}$$ What is the logic and thought process from using the respective even and odd properties, $$\begin{align*} f(-x) &amp;= f(x)\\    f(-x) &amp;= -f(x) \end{align*}$$   to derive $E(x)$ and $O(x)$?    The best I get to is: For even: $f(x)-f(-x)=0$ and for odd: $f(x)+f(-x)=0$  Given the definition of $E(x)$ and $O(x)$, it makes a lot of sense (hindsight usually is) but starting from just the properties. Wow, I feel I'm missing something crucial. Duplicating a mesh object Overstaying on a US Visa Waiver Program A friend of mine came from Australia on the WVP and stayed 92 days. I made a mistake booking Her flight scheduling a Saturday arrival/departure at DFW. This amounted to a 92 day stay and with no funds to rebook a low cost flight through Qantas it was necessary to leave on the scheduled flight.   Question # 1) Was a automatic I-94W submitted by the airlines? She had no customs forms to fill out upon departure.   Question #2) How does this effect another WVP being issued if applied for? Word for someone who acts like an expert but who has very little knowledge? What is a word to describe an individual who acts like an expert in a subject area, constantly stating facts and correcting people, but who actually has very little knowledge on the subject? Is there a formal proof for the superposition theorem? What am I doing wrong? Joint Density of sum of random variables! So, I have this question:    And, what I have tried so far is I let $z_1 = \frac{X + Y}{2}$ and let $z_2 = \frac{X - Y}{2}$ to use change of variables for this question. However, when I work this out and plug it into my joint distribution of $X$ and $Y$ above, I end up with the $z_2$ disappearing and only having $z_1$ left in my joint distribution of $z_1$ and $z_2$. So, then when I go to find the marginal for just $z_1$ (which is $\frac{X + Y}{2}$ &lt;- what I am looking for), there is no $z_2$ therefore, integrating wrt to $z_2$, I get $z_2$ just come up (integral of 1). This is an issue because the bounds are from 0 to $\inf$. Obviously, I can't have infinite in my marginal density so what am I doing wrong?   Also, for question 5, I work it out similarly except I let $z_2 = X$ but I just end up with the exact same density as $f_{x,y}$ as seen in question 4 - is that normal? Please help, I been doing this question for a long time trying various dummy transformations.  Also, for question 4, I found the marginals of $x$ and $y$ and realized that the independence consequence (of the product being equal to the joint) is satisfied but using convolution, I get the same issue of my integral coming out to infinite! Thank you for all the help!   EDIT: Am I doing my bounds wrong? the bound for z_2 is from 0 to inf or 0 to z_1? Travelling as an unmarried Western couple in Indonesia How do I calculate the closest power of 2 or 10 a number is? What is the most efficient way to cacluate the closest power of a 2 or 10 to another number? e.g.  3.5 would return 4 for power of 2 and 1 for power of 10  123 would return 128 for power of 2 and 100 for power of 10  0.24 would return 0.25 for power of 2 and 0.1 for power of 10  I'm just looking for the algorithm and don't mind the language. MacBook Pro (15-inch, 2016) with 2 USB-C to HDMI adapters. The setup works great if I start up in that configuration.   If I connect the adapters while the machine is running or simply sleeping, one of the monitors will never get a signal and stay in low power mode. The OS sees the monitor, it shows in the display arrangement settings and I can move the mouse into it, but until I restart, I can't see anything on it.  Once I have restarted I can let the machine sleep or whatever, and the display still works unless I disconnect the adapter. As soon as I do that a restart is required to use it again.   Using MacOS Sierra (10.12.4)  Using this adapter: New questions, Show Recommended, Sort Newest not working When may adjectives precede determiners? (E.g. too difficult a task) The expression too difficult a task sounds a little pompous, but it doesn't sound ungrammatical. According to my folk-beliefs about English grammar, determiners precede adjectives. However, the expression too difficult a task seems to controvert that belief.  Additionally, the expression too difficult of a task seems grammatical too.    Under what conditions may determiners precede adjectives? Are there conditions under which too difficult of a task would be a more grammatical expression than too difficult a task would be?   (This question does not ask what the question “How big of a problem” vs. “how big a problem” asks. That question does not pertain to determiners.) There is this addon that was built called Window Generator 2. It can be . However, when I go to the download link it shows up in a new tab as a bunch of code.  How can I download and use this addon in Blender? Gradle compiling slows down my computer The responsiveness is really bad on a newly installed Ubuntu 14.04 LTS.  Here's the specs of my laptop:  Quadcore Intel i7-4600U CPU @ 2.10GHz 12GB Ram 1TB Samsung EVO SSD   And when gradle is compiling, my entire system slows to a crawl, videos begin stuttering, browser scrolling lags... etc.  The same goes when a page refresh occurs in another window in Chrome, and while it refreshes, the HTML5 video in another tab begins stuttering.  How can I fix this?  Here are some logs:  $ vmstat -a 1 5 -   $ iostat -x 1 5 -   $ top -b - Prove that for every $n\geq m \geq1$ natural numbers, the following number is an integer:  $${\gcd(n,m)\over n}\cdot{n\choose m}$$  Where $\gcd$ is the greatest common divisor.  I tried to make it simpler by cancelling the $n$ from the left side, and making it $(n-1)!$ on the right: $\gcd(n, m) \cdot \frac{(n-1)!}{m!(n-m)!}$, but can't really go further.   This was problem B-2 on the . What size should the HMAC key be with SHA-256? I'm trying to generate a secret key to be used for HMAC SHA-256 signature processing. I've seen many sample of keys with variable length from 32 characters to 96 characters.  What is the ironclad rule for this key size? Why isn't $V= V_1 + V_2$? $V=V_a - V_c = V_a - V_b + V_b - V_c$, $V_a - V_b= V_1$ and $V_b - V_c = V_2$ Doesn't that prove that $V = V_1 + V_2$? Regardless of $V_3$, If i'm wrong , is there a way to obtain $V$ in terms of $V_1$, $V_2$ and $V_3$