deletions | additions       diff --git a/ratio.tex b/ratio.tex  index 838ef88..912e620 100644  --- a/ratio.tex  +++ b/ratio.tex 
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Using the above answer, we know that $S$ \\  \vspace{1em}  $L=\frac{9}{4} > 1$ : $S$ Diverges \\  Using the Ratio Test, determine the largest integer value of $x$ for which   the following series converges:  \begin{align}  \sum^{\inf}_{n=1} \frac{(n\:+\:1)\cdot x^n}{2\cdot3^{n}}  \end{align}  ∞  ∑ (n + 1)x^n/2*3^n  n=1  lim |a(n + 1) ÷ a(n)| < 1  n→∞  \end{document}