DescriptionRatio test proof.svg	English: A plot showing how the ratio test test is proven in the convergent case. Given a sequence like the blue one, for which the ratio of adjacent terms ${\displaystyle |a_{n+1}/a_{n}|}$ converges to L < 1, we identify a ratio r = (L+1)/2 and show that for large enough n the sequence is dominated by the simple geometric sequence rk. In this case the ratio of adjacent terms of the blue sequence converges to L=1/2, so we choose r=3/4, and rk dominates for all n ≥ 2. Source used to generate this chart is shown below.
Date	24 March 2013
Source	Own work   This W3C-unspecified diagram was created with Mathematica.
Author	User:Dcoetzee

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Mathematica source to generate graph (which was then saved as SVG from Mathematica):

Show[][][(3/4)^n, {n, 1, 15}], 
  PlotStyle -> {Hue[0], PointSize[Large]}], 
 ListPlot[][(n + 1)/n * (1/2)^n, {n, 1, 15}], 
  PlotStyle -> PointSize[Large],
 PlotRange -> All, AxesStyle -> FontSize -> 14]

LaTeX source for labels:

$$ \left(\frac{3}{4}\right)^n $$
$$ \frac{n+1}{n}\left(\frac{1}{2}\right)^n $$

These were converted to SVG with [1] and then the graph was embedded into the resulting document in Inkscape. Axis fonts were also converted to Liberation Serif and the legend was added in Inkscape.