How does Zonal statistics handle pixels that are on border of polygon?
How does QGIS Zonal Statistics handle partially overlapping pixels?
How can I create an Excel spreadsheet with C# without requiring Excel to be installed on the machine that's running the code? I've just had to write a string reverse function in C# 2.0 (i.e. LINQ not available) and came up with this:  public string Reverse(string text) {     char[] cArray = text.ToCharArray();     string reverse = String.Empty;     for (int i = cArray.Length - 1; i &gt; -1; i--)     {         reverse += cArray[i];     }     return reverse; }   Personally I'm not crazy about the function and am convinced that there's a better way to do it. Is there? I have a Godox X2Tc and a Godox X1Rc. I want to control my Canon Speedlite 430 EXII. (I also have a Godox V1, which is a beautiful thing!) I have the Canon Speedlite attached to the Godox receiver, so it should fire. It just wont! How do I set it up correctly so the receiver makes the Canon Speedlite fire?  Update: Michael C answered this question. I had the ID numbers set differently on the transmitter and receiver. I made them the same and now it all works. Perfect! Thanks Michael!! How to measure supply currents ranging from 1μA to 10mA? integral of $\int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx$ using contour integration? I have an interest in contour integration. I am not that good at it, but I enjoy learning what I can about it.  Here is a version of a rational log integral rarely encountered.  $\displaystyle \int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx=\frac{3}{4}\ln^{2}(2)-\frac{{\pi}^{2}}{48}$  I can do this using real methods (via double integral and substitution). I can post my workings if anyone would be interested.  My question is, can this be evaluated using contour integration due to the limits being $[0,1]$ instead of $[0,\infty)$?.  Contours may not be the most efficient way to go about it, but what is the course of action when the limits are 0 to 1 instead of 0 to infinity?. Performing Point Distance analysis using Basic level license of ArcGIS Desktop? I am using ArcView (ArcGIS Desktop Basic) 10.1 and I need to perform a point distance analysis.   What are the steps to determine the distance from A to B-Z, B to A-Z, C to A-Z, etc? I have several thousand nodes of a particular content type. Using the web interface (example.com/admin/content), I can only delete about 50 at a time. How can I quickly delete them? Is the Ubuntu Phone available anywhere yet? I want start developing apps.  I am very impatient to start to develop on real ubuntu phone. How to render a background image in 2.8? Prove that if $\sum{a_n}$ converges absolutely, then $\sum{a_n^2}$ converges absolutely I'm trying to re-learn my undergrad math, and I'm using Stephen Abbot's Understanding Analysis. In section 2.7, he has the following exercise:  Exercise 2.7.5 (a) Show that if $\sum{a_n}$ converges absolutely, then $\sum{a_n^2}$ also converges absolutely. Does this proposition hold without absolute convergence?  I'm posting about this here because my answer to that last question about whether the proposition holds without absolute convergence is "Yes", but my suspicions are raised by him merely asking the question. Usually questions like this are asked to point out that certain conditions are necessary in the statement of propositions, theorems, etc. I just want to see if I'm missing something here.  Anyway, here's how I prove the absolute convergence of $\sum{a_n^2}$, and note that I never use the fact that $\sum{a_n}$ is absolutely convergent:  Proof: Let $s_n = \sum_{i=1}^n{a_n^2}$. I want to show that $(s_n)$ is a Cauchy sequence. So, let $\epsilon &gt; 0$ and $n &gt; m$, and consider, \begin{equation}   \begin{aligned}     |s_n - s_m| &amp;= |(a_1^2 + a_2^2 + \cdots a_n^2) - (a_1^2 + a_2^2 + \cdots a_m^2)|\\                 &amp;= |(a_{m+1})^2 + (a_{m+2})^2 + \cdots + a_n^2|\\                 &amp;= |a_{m+1}|^2 + |a_{m+2}|^2 + \cdots + |a_n|^2\\   \end{aligned} \end{equation} Now, since $\sum{a_m}$ converges, the sequence $(a_m)$ has limit 0. Therefore I can choose an $N$ such that $|a_m| &lt; \sqrt{\epsilon/n}$ for all $m &gt; N$. So for all $n &gt; m&gt; N$,  we have, \begin{equation}   \begin{aligned}     |s_n - s_m| &amp;= |a_{m+1}|^2 + |a_{m+2}|^2 + \cdots + |a_n|^2\\                 &amp;&lt; \left(\sqrt{\frac{\epsilon}{n}}\right)^2 + \left(\sqrt{\frac{\epsilon}{n}}\right)^2 + \cdots + \left(\sqrt{\frac{\epsilon}{n}}\right)^2\\                 &amp;&lt; \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2 + \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2 + \cdots + \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2\\                 &amp;= \epsilon   \end{aligned} \end{equation} Therefore $(s_n)$ is Cauchy and $\sum{a_n^2}$ converges. And since $\sum{a_n^2} = \sum{|a_n^2|}$, the series $\sum{a_n^2}$ is absolutely convergent. &#x220E;  Am I doing something wrong here? Am I right in thinking that $\sum{a_n}$ need not be absolutely convergent for $\sum{a_n^2}$ to be absolutely convergent? Prove by Mathematical Induction: $1(1!) + 2(2!) + \cdot \cdot \cdot +n(n!) = (n+1)!-1$ Prove by Mathematical Induction . . .  $1(1!) + 2(2!) + \cdot \cdot \cdot +n(n!) = (n+1)!-1$  I tried solving it, but I got stuck near the end . . .  a. Basis Step:      $(1)(1!) = (1+1)!-1$      $1 = (2\cdot1)-1$      $1 = 1 \checkmark$   b. Inductive Hypothesis     $1(1!) + 2(2!) + \cdot \cdot \cdot +k(k!) = (k+1)!-1$   Prove k+1 is true.     $1(1!) + 2(2!) + \cdot \cdot \cdot +(k+1)(k+1)! = (k+2)!-1$      $\big[RHS\big]$      $(k+2)!-1 = (k+2)(k+1)k!-1$      $\big[LHS\big]$      $=\underbrace{1(1!) + 2(2!) + \cdot \cdot \cdot + k(k+1)!} + (k+1)(k+1)!$ (Explicit Last Step)      $= \underbrace{(k+1)!-1}+(k+1)(k+1)!$ (Inductive Hypothesis Substitution)      $= (k+1)!-1 + (k+1)(k+1)k!$      $= (k+1)k!-1 + (k+1)^{2}k!$   My [LHS] looks nothing like my [RHS] did I do something wrong?  EDIT:     $ = (k+1)k! + (k+1)^2k! -1 $      $ = (k+1)(k!)(1 + (k+1))-1$      $ = (k+1)(k!)(k+2)-1 = (k+2)(k+1)k!-1$ How to print without newline or space? Dynamic grid with Atlas generation What are the English laws on bringing pets into the country? What is the function of this circuit? Just wondering if someone can give me an explanation for this capacitor layout - what is it's function? The chip to the right is an ADC.  Circled in blue.    I'm guessing it is well known but i don't know how to search for it. How to apply multiple format to a list How do you add an ActionListener onto a JButton in Java My chain broke and in a moment of silliness (I was cold wet and slightly annoyed)  I threw the broken one away before thinking about measuring the new one.  Is there a guide to getting the chain length/tension correct ?  It's an 8 speed road bike (Shimano Sora back, double ring front) When to delete your 0 vote answers? I've been in the SO community a little over a month now - and having a great time!  As I grow into a contributing citizen of stackoverflow, i'd like to ensure that i'm being responsible with my answers.   I've answered a few questions, some without upvotes, some voted on and some accepted.  I feel that after a certain period of time, 0 vote answers are probably providing more clutter than value.  Apparently, nobody has found them useful, so they probably aren't (or are poorly written). Tonight I went through and deleted my answers with 0 upvotes where some answer was accepted.  That was an easy decision.   I left my 0 vote answers where nothing was accepted yet, well, because I think they could provide the information that the OP requested.  But at some point, I think my answers might just be cluttering the issue.  So my question to you is: How do you know when it's time to delete your 0 vote answers?  Or even 1 vote answers for that matter? I know how to CALCULATE dot product, but still don't understand MEANING of it.  I mean, If I have to explain vector addition I would say that "Sum of two vectors give you the third vector that has the same effect as other two combined"  But I don't know how to explain dot product. For example we have two vectors: v=(3,1) and w=(2,4). Dot product of these two is 3*2 + 1*4 = 10. What does this result (10) tell us?