deletions | additions       diff --git a/ratio.tex b/ratio.tex  index 3d1f9d5..0598f35 100644  --- a/ratio.tex  +++ b/ratio.tex 
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\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]  \lim_{n\to\infty}\left|\:\frac{3x \left(1\:+\:\frac{2}{n}\right)}{\left(1\:+\:\frac{1}{n}\right)}\:\right|\hspace{1em}<\hspace{1em}1 \\[1em]  \end{align}