shows standard computation time exceeded :| .. as usual :P ... @Chris'ssis .. does it have a nice closed form .. I mean free of Li and stuff like that ?
Hi, soft off topic: Given a sequence $x_n$ defined as follows: $x_1 = 1, x_{n+1}= \sqrt (x_n + 3)$, why does one need to show that $\lim x_n $ exists before finding the limit? If I can show $\lim x_n = (1+\sqrt 13)/2, doesn't that imply that the limit exists (since it's equal to a real number)?
@TheSubstitute yes inherently if you prove by the definition of a limit that it is $L$ then that is a prove that it exists and is equal to $L$. Proving existence firsthand w/o finding the actual limit allows one to use other methods to find the actual limit. For instance for your $x_n$ support I prove that the limit exists (i.e. $x_n$ converges to a real number) then I can say $L = \sqrt{L+3} \implies L^2 - L - 3 = 0$ and then we can solve that quadratic and pick the appropriate solution.
yep, the russian Wladimir Klitschko is about to set a world record for most title defenses by a heavy weight
Klitschko is the longest reigning IBF, WBO & IBO heavyweight champion in history with the most title defenses for those organizations. Overall, he is the second longest reigning Heavyweight Champion of all time with the second most successful grand total title defenses with 21 (including his "super" title recognition).
Now, I'm going to create something very special ...
Till then, there is a nother interesting piece to try $$\sum_{n=1}^{\infty} \frac{H_n}{n^2} \left(1-\frac{1}{3}+\frac{1}{5}-\cdots +\frac{(-1)^{n+1} }{2n-1}\right)$$
@Chris'ssis Given the main answer to the interview riddle, which seems totally correct, i'm starting to wonder whether the answer they gave you is the right one ...
Proposed Q&A site for this site is for any part of Trolling. For those who want to prevent trolling, design systems that discourage trolling, or for people who want to successfully troll others.
@robjohn I only partially understood the contents of the link that Steven Stadnicki linked to in the comment :| ... but getting the asymptotics for the expression with $x$ shouldn't be too difficult ... imho :-)
Can we prove that given an entire function $f$ that is also one to one then $f$ must be linear?
Thanks for any help.
Prove that
\begin{equation}
\prod_{k=1}^{\lfloor (n-1)/2 \rfloor}\tan \left(\frac{k \pi}{n}\right)= \left\{
\begin{aligned}
\sqrt{n} \space \space \text{for $n$ odd}\\
\\
\ 1 \space \space \text{for $n$ even}\\
\end{aligned}
\right.
\end{equation}
I foun...
