User:GFauxPas/Sandbox

Welcome to my sandbox, you are free to play here as long as you don't track sand onto the main wiki. --GFauxPas 09:28, 7 November 2011 (CST)


 * $u \ v \ \mathsf{u} \ \mathsf{v} \ \nu \ \upsilon$

Anyone else have a hard time distinguishing between $u$ and $v$? I would like it to look more like this, does it confuse anyone else? It seems PW doesn't have the upgreek package. --GFauxPas 07:49, 27 January 2012 (EST)


 * Nope. Multiple years of extensive TeX writing and reading have trained my eye. I agree that referenced $v$ looks more distinguished, but imagine it is hard to implement. --Lord_Farin 08:08, 27 January 2012 (EST)

Convergence
Does this proof work for $a_n \in \C$? I don't know if you can use the ratio test for complex stuff.

Taking the limit as $n \to +\infty$:
 * $\displaystyle \left|{\frac{n+1}{n-k+1}}\right|$ converges to $1$


 * $\displaystyle \left|\frac{n^k}{ \left({n+1}\right)^k}\right|$ converges to $1$


 * $\displaystyle \left |{\frac{ {a_{n+1} }^{k-1} } { {a_n}^{k-1} } }\right|$ converges to some number $<1$ because $a_n$ is by hypothesis convergent and therefore Cauchy. Right? Does that work?

--GFauxPas 12:38, 4 March 2012 (EST)