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Convergence: Ratio Test

Let $\sum{a_{k}}$ be a series with positive terms and suppose that:

$$ \lim_{k\mapsto\infty}=\frac{a_{k+1}}{a_{k}}=L $$

then:

  • if $L \lt 1$ then $\sum{a_{k}}$ converges
  • if $L \gt 1$ then $\sum{a_{k}}$ diverges
  • if $L = 1$ then the test is inconclusive
fuss/mathematics/calculus/series/convergence/positive.txt ยท Last modified: by 127.0.0.1
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