# Ratio Test

Given an infinite series $$S$$
$S = \sum_{i=0}^\infty s_i$
for which the limit of the absolute value of the ratio of $$s_{n+1}$$ to $$s_n$$ converges to a value $$r$$ as $$n$$ tends to infinity
$r = \lim_{n \to \infty} \left|\frac{s_{n+1}}{s_n}\right|$
then if $$r$$ is less than one the series converges and if it is greater than one it diverges. If it equals one then no conclusion can be drawn from the test.

### Gallimaufry

 AKCalc ECMA Endarkenment Turning Sixteen

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