BC Calc III
Sample Quiz 9.1-9.4
Name:
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#1.
Complete (no work necessary):

a
a. An example of a divergent series
n 1
n
with an  0 is given by an 

b. Look at the series
a
k 1
k
. The ratio test states that if
, then the series converges.

c. An expression of the form
a
k 1
k
is called an
.
Corresponding to this, we have the sequence {Sn}, which is called the
. The nth term of this sequence is given by Sn =
The sequence {an} is called
If lim ak  0 then
k 
.
.
k 2
.
k 
k 1
Use this to determine whether the series converges or diverges. If the series converges,
find the value.

#2. Find an expression for the sequence of partial sums, S n , for the series
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 ln 
.
#3.
Determine whether each series converges or diverges. Justify your answer
carefully and completely

n3
a.  2
n + n
n2
 n2  1 
 n 
n  1 3


b.
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#3. (continued)Determine whether each series converges or diverges. Justify your answer
carefully and completely
c.

 n! n!
n 1
(2n)!


d.
k 1
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k
e
k2
 n2  1 
Determine whether the sequence an  tan 1 
 converges or diverges. Explain.
 n 
If it converges, find the limit.
#4.

#5.
Find the value of n such that S n approximates the value of the series
an error of at most .001. Explain carefully.
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k
k 1
1
with
1
2

#6. Look at the series
(1) n
 n 3
n 1
n
.
a. Show that this series converges.
b. Find a value for n such that Sn is within .001 of the actual sum.
#7. Determine whether the following series converges conditionally, converges
absolutely, or diverges? Show all steps/explain.


n 1
(1)n  2n
n3
BC CALC III