this is for holding javascript data
redthumb edited ratio.tex
over 9 years ago
Commit id: 9c2c86320d9c084d1da34c5ac6c4696f49706936
deletions | additions
diff --git a/ratio.tex b/ratio.tex
index 3f7f383..d11af97 100644
--- a/ratio.tex
+++ b/ratio.tex
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\:&=\:\lim_{n\to\infty}\left|\:\frac{9}{(n\:+\:2)\cdot2^{(2n\:+\:1)}}\hspace{1em}\cdot\hspace{1em}\frac{(n\:+\:1)\cdot2^{(2n\:-\:1)}}{1}\:\right| \\[1em]
\:&=\:\lim_{n\to\infty}\left|\:\frac{9}{(n\:+\:2)}\hspace{1em}\cdot\hspace{1em}\frac{(n\:+\:1)\cdot2^{(2n\:-\:1)}\cdot2^{-(2n\:+\:1)}}{1}\:\right| \\[1em]
\:&=\:\lim_{n\to\infty}\left|\:\frac{9}{(n\:+\:2)}\hspace{1em}\cdot\hspace{1em}\frac{(n\:+\:1)\cdot2^{(2n\:-\:1)}\cdot2^{(-2n\:-\:1)}}{1}\:\right| \\[1em]
\:&=\:\lim_{n\to\infty}\left|\:\frac{9}{(n\:+\:2)}\hspace{1em}\cdot\hspace{1em}\frac{(n\:+\:1)\cdot2^{(2n\:-\:1\:-2n\:-\:1)}}{1}\:\right| \\[1em]
\end{align}
\end{document}