deletions | additions       diff --git a/ratio.tex b/ratio.tex  index a6d1025..a463c62 100644  --- a/ratio.tex  +++ b/ratio.tex 
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What is the radius of convergence for the series:  \begin{align}  \sum^{\infty}_{n=0} \frac{x^n}{(n\:+\:1)} \frac{x^n}{(n\:+\:1)!}  \end{align}  Apply Ratio Test:  \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} \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] \end{align}  \end{document}