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