this is for holding javascript data
redthumb edited ratio.tex
over 9 years ago
Commit id: f84b70d10de22f467c1bc6a268218d879754cd23
deletions | additions
diff --git a/ratio.tex b/ratio.tex
index 361c8be..9136ec1 100644
--- a/ratio.tex
+++ b/ratio.tex
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\lim_{n\to\infty}\left|\:\frac{(n\:+\:1)\cdot x}{2\cdot3^{(n\:+\:1)}}\hspace{1em}\cdot\hspace{1em}\frac{2\cdot3^{n}}{(n\:+\:1)}\:\right|\hspace{1em}<\hspace{1em}1 \\[1em]
\lim_{n\to\infty}\left|\:\frac{(n\:+\:1)\cdot x}{2}\hspace{1em}\cdot\hspace{1em}\frac{2\cdot3^{n}\cdot3^{-(n\:+\:1)}}{(n\:+\:1)}\:\right|\hspace{1em}<\hspace{1em}1 \\[1em]
\lim_{n\to\infty}\left|\:\frac{(n\:+\:1)\cdot x}{2}\hspace{1em}\cdot\hspace{1em}\frac{2\cdot3^{n}\cdot3^{(-n\:-\:1)}}{(n\:+\:1)}\:\right|\hspace{1em}<\hspace{1em}1 \\[1em]
\lim_{n\to\infty}\left|\:\frac{(n\:+\:1)\cdot x}{2}\hspace{1em}\cdot\hspace{1em}\frac{2\cdot3^{(n\:-n\:-\:1)}}{(n\:+\:1)}\:\right|\hspace{1em}<\hspace{1em}1 \\[1em]
\end{align}
% \lim_{n\to\infty}\left|\:\frac{(n\:+\:1)\cdot x}{2}\hspace{1em}\cdot\hspace{1em}\frac{2\cdot3^{n}\cdot3^{(-n\:-\:1\:+\:n\:+\:1)}\:\right|\hspace{1em}<\hspace{1em}1 \\[1em]
\end{document}