deletions | additions       diff --git a/ratio.tex b/ratio.tex  index a463c62..23855c8 100644  --- a/ratio.tex  +++ b/ratio.tex 
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\begin{align}  \lim_{n\to\infty}\left|\:a(n\:+\:1)\hspace{1em}\div\hspace{1em}a(n)\:\right|\hspace{1em}<\hspace{1em} 1 \\[1em]  \lim_{n\to\infty}\left|\:\frac{x^{(n\:+\:1)}}{(n\:+\:1\:+\:1)!}\hspace{1em}\div\hspace{1em}\frac{x^n}{(n\:+\:1)!}\:\right|\hspace{1em}<\hspace{1em} 1 \\[1em]  \lim_{n\to\infty}\left|\:\frac{x^{(n\:+\:1)}}{(n\:+\:2)!}\hspace{1em}\div\hspace{1em}\frac{x^n}{(n\:+\:1)!}\:\right|\hspace{1em}<\hspace{1em} 1 \\[1em]  \lim_{n\to\infty}\left|\:\frac{x^{(n\:+\:1)}}{(n\:+\:2)!}\hspace{1em}\cdot \hspace{1em}\frac{(n\:+\:1)!}{x^n}\:\right|\hspace{1em}<\hspace{1em} 1 \\[1em]  \end{align}  \end{document}