deletions | additions       diff --git a/ratio.tex b/ratio.tex  index 6278894..add97fc 100644  --- a/ratio.tex  +++ b/ratio.tex 
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\begin{document}  Let:  \begin{align}  S=\sum^{\infty}_{n=1} n\cdot\left(\frac{5}{4}\right)^{(2n\:+\:1)}  \end{align}  If I use the Ratio Test to determine whether S converges, I need to   determine:  \begin{align}  \lim_{n\to\infty}\left|\:a(n\:+\:1)\hspace{1em}\div\hspace{1em}a(n)\:\right|  \end{align}    What is the value of this limit?  \begin{align}  L=\lim_{n\to\infty}\left|\:a(n\:+\:1)\hspace{1em}\div\hspace{1em}a(n)\:\right| \\ \\[1em]  L=\lim_{n\to\infty}\left|\:(n\:+\:1)\cdot\left(\frac{5}{4}\right)^{(2(n\:+\:1)\:+\:1)}\hspace{1em}\div\hspace{1em}n\cdot\left(\frac{5}{4}\right)^{(2n\:+\:1)}\:\right| \\  L=\lim_{n\to\infty}\left|\:(n\:+\:1)\cdot\left(\frac{5}{4}\right)^{(2n\:+\:2\:+\:1)}\hspace{1em}\div\hspace{1em}n\cdot\left(\frac{5}{4}\right)^{(2n\:+\:1)}\:\right| \\  L=\lim_{n\to\infty}\left|\:(n\:+\:1)\cdot\left(\frac{5}{4}\right)^{(2n\:+\:3)}\hspace{1em}\div\hspace{1em}n\cdot\left(\frac{5}{4}\right)^{(2n\:+\:1)}\:\right| \\