Latex on Karpoke - Just Another Blog

0.999...=1

Wed, 18 May 2011 14:21:00 +0100

$$ \begin{align*} \frac{1}{3} &= 0.\stackrel{\frown}{3} \\ \frac{1}{3} &= 0.333\dots \\ 3 \cdot \frac{1}{3} &= 3 \cdot 0.333\dots \\ 1 &= 0.999\dots \\ 1 &= 0.\stackrel{\frown}{9} \end{align*} $$

0!=1!

Wed, 18 May 2011 14:07:00 +0100

$$ \begin{align*} n! &= n \cdot (n-1) \cdot (n-2) \cdots 3 \cdot 2 \cdot 1 \\ n! &= n \cdot (n-1)! \\ (n-1)! &= \frac{n!}{n} \end{align*} $$

Si tomamos $n=1$:

$$ \begin{align*} (1-1)! &= \frac{1!}{1} \\ 0! &= 1 \end{align*} $$

LaTeX en Wordpress

Tue, 29 Mar 2011 18:54:00 +0100

Descarga el plugin de LaTeX para Wordpress. Luego, escribe:

\begin{align*}
ax^2+bx+c &= 0 \\
x^2+\frac{b}{a}x+\frac{c}{a} &= 0 \\
x^2+\frac{b}{a}x &= -\frac{c}{a} \\
x^2+\frac{b}{a}x+\frac{b^2}{4a^2} &= \frac{b^2}{4a^2} - \frac{c}{a} \\
(x+\frac{b}{2a})^2 &= \frac{b^2}{4a^2} - \frac{4ac}{4a^2} \\
x+\frac{b}{2a} &= \pm\sqrt{\frac{b^2-4ac}{4a^2}} \\
x+\frac{b}{2a} &= \frac{\pm\sqrt{b^2-4ac}}{2a} \\
x &= \frac{-b\pm\sqrt{b^2-4ac}}{2a}
\end{align*}

El resultado será parecido a éste:

$$ \begin{align*} ax^2+bx+c &= 0 \\ x^2+\frac{b}{a}x+\frac{c}{a} &= 0 \\ x^2+\frac{b}{a}x &= -\frac{c}{a} \\ x^2+\frac{b}{a}x+\frac{b^2}{4a^2} &= \frac{b^2}{4a^2} - \frac{c}{a} \\ (x+\frac{b}{2a})^2 &= \frac{b^2}{4a^2} - \frac{4ac}{4a^2} \\ x+\frac{b}{2a} &= \pm\sqrt{\frac{b^2-4ac}{4a^2}} \\ x+\frac{b}{2a} &= \frac{\pm\sqrt{b^2-4ac}}{2a} \\ x &= \frac{-b\pm\sqrt{b^2-4ac}}{2a} \end{align*} $$