this is for holding javascript data
redthumb edited ratio.tex
over 9 years ago
Commit id: ada323bf7520e3a29a79b1fc4dcb8b3c99bcf1ad
deletions | additions
diff --git a/ratio.tex b/ratio.tex
index 351c877..fb4e2e4 100644
--- a/ratio.tex
+++ b/ratio.tex
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\:&=\:\lim_{n\to\infty}\left|\:\frac{9^\left(n\:+\:1\right)}{(n\:+\:2)\cdot2^{(2n\:+\:1)}}\hspace{1em}\cdot\hspace{1em}\frac{(n\:+\:1)\cdot2^{(2n\:-\:1)}}{9^n}\:\right| \\[1em]
\:&=\:\lim_{n\to\infty}\left|\:\frac{9^\left(n\:+\:1\right)\cdot9^{(-n)}}{(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^{\left(n\:+\:1\:-\:n\right)}}{(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^{(1)}}{(n\:+\:2)\cdot2^{(2n\:+\:1)}}\hspace{1em}\cdot\hspace{1em}\frac{(n\:+\:1)\cdot2^{(2n\:-\:1)}}{1}\:\right| \\[1em]
\end{align}
\end{document}