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 · Last modified: 2022/04/19 08:28 by 127.0.0.1

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