8.5 Ratio Test

8.5 Ratio Test - 8 .5 
R a t io 
T e s t 
...

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Unformatted text preview: 8 .5 
R a t io 
T e s t 
 Def:

Let
 ∑a n 
be
a
series
with
positive
terms
and
suppose
 an +1 lim = ρ .


 that
 n → ∞ a n 1. The
series
converges
if
 ρ < 1.
 2. The
series
diverges
if
 ρ > 1
or
 ρ 
is
infinite.
 3. The
test
is
inconclusive
if
 ρ = 1.
 ∞ 5n Ex.
 ∑ n 3 
 n =1 
 
 
 
 
 ∞ 5n Ex.
 ∑ n! 
 n =1 
 
 
 
 n+2 Ex.
 ∑ 5 n 2 + 3 
 n =1 ∞ 
 
 
 
 
 
 
 
 
 
 Do:

Use
the
ratio
test
to
determine
if
the
following
series
 converges
or
diverges.
 ∞ 

 
 
 
 n ⎛ 1⎞ ∑ n⎝ 2⎠ 
 n =1 ...
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