0.999...=1

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

May 18, 2011 · 1 min · 27 palabras · Nacho Cano

0!=1!

$$ \begin{align*} n! &= n \cdot (n-1) \cdot (n-2) \cdots 3 \cdot 2 \cdot 1 \\ n! &= n \cdot (n-1)! \\ (n-1)! &= \frac{n!}{n} \end{align*} $$ Si tomamos $n=1$: $$ \begin{align*} (1-1)! &= \frac{1!}{1} \\ 0! &= 1 \end{align*} $$

May 18, 2011 · 1 min · 41 palabras · Nacho Cano

LaTeX en Wordpress

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

March 29, 2011 · 1 min · 91 palabras · Nacho Cano