3
$\begingroup$

I don't understand the explanation for k & n in my text book. What are they trying to say by "... for any n consecutive values of k"? In the 1st formula, it says $k=0,1,2,\ldots,n-1$ then next it says $k=n,n+1,\ldots,2n-1$, that will mean $k=1,2,3,\ldots,2n-1$?

http://i.imgur.com/3HoQd.png

  • 0
    It means the formula holds when you plug in $k=n$, or plug in $k=n+1$, or $k=n+2$, or $\dots$ $k=2n-1$; it doesn 't matter what $n$ is but it is apparently fixed from the beginning. Note that these are all consecutive integers and there are $n$ of them.2011-11-23
  • 0
    So suppose I have $(\cos{\theta}+i\cdot \sin{\theta})^{\frac{1}{6}}$. Then I can set $k=6 \text{ or 7,8,...,11}$. But according to the 1st formula, won't it be best I let $k=0$ then I'd just have $\cos{\frac{\theta}{n}+i\cdot \sin{\frac{\theta}{n}}}$?2011-11-23
  • 0
    What do you mean by "best"? It's just saying it works for any integer $k$, not saying what's "best."2011-11-23
  • 0
    I mean if I let $k=0$, I will cancel out $2k\pi$?2011-11-23
  • 0
    Well yes, for $k=0$ we have that $2k\pi=0$ and so vanishes out. I don't see the relevance of that to your question though.2011-11-23
  • 0
    Sorry for going off-topic, but three small things: 1. It would be better to use the built-in image upload functionality because the image is then uploaded to a server hosted by StackExchange (you can do so by hitting `ctrl-G` or clicking on the `Image ` button on top of the "ask a question view" and following the instructions). 2. It looks a bit better if you use `\ldots` instead of `...`, because TeX then takes care of proper spacing. 3. It is *explanation*, not *explaination*.2011-11-23

2 Answers 2