this is for holding javascript data
redthumb edited ratio.tex
over 9 years ago
Commit id: 333ad39d6698afe9a47746dd12b7e5aea981283e
deletions | additions
diff --git a/ratio.tex b/ratio.tex
index f56cb56..3d1f9d5 100644
--- a/ratio.tex
+++ b/ratio.tex
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\lim_{n\to\infty}\left|\:\frac{(n\:+\:2)\cdot x}{2}\hspace{1em}\cdot\hspace{1em}\frac{2\cdot3^{(1)}}{(n\:+\:1)}\:\right|\hspace{1em}<\hspace{1em}1 \\[1em]
\lim_{n\to\infty}\left|\:\frac{(n\:+\:2)\cdot x}{2}\hspace{1em}\cdot\hspace{1em}\frac{2\cdot3}{(n\:+\:1)}\:\right|\hspace{1em}<\hspace{1em}1 \\[1em]
\lim_{n\to\infty}\left|\:\frac{(n\:+\:2)\cdot x}{2}\hspace{1em}\cdot\hspace{1em}\frac{6}{(n\:+\:1)}\:\right|\hspace{1em}<\hspace{1em}1 \\[1em]
\lim_{n\to\infty}\left|\:\frac{6(n\:+\:2)\cdot x}{2(n\:+\:1)}\:\right|\hspace{1em}<\hspace{1em}1 \lim_{n\to\infty}\left|\:\frac{6x(n\:+\:2)}{2(n\:+\:1)}\:\right|\hspace{1em}<\hspace{1em}1 \\[1em]
\lim_{n\to\infty}\left|\:\frac{3x(n\:+\:2)}{(n\:+\:1)}\:\right|\hspace{1em}<\hspace{1em}1 \\[1em]
\lim_{n\to\infty}\left|\:\frac{3x\cdot n\left(\frac{n}{n}\:+\:\frac{2}{n}\right)}{n\left(\frac{n}{n}\:+\:\frac{1}{n}\right)}\:\right|\hspace{1em}<\hspace{1em}1 \\[1em]
\end{align}