Math 203 Fall 2006                                                                                                 Name: __________________________
Test 3 Series                                                                                                            Date: _____________




1.
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit.

an =
A.
Sequence converges to 0
B.
Sequence diverges
C.
Sequence converges to 1
D.
Sequence converges to -1
E.
Sequence diverges to 1


2.
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit.

an =
A.
Sequence converges to 1
B.
Sequence converges to 0
C.
Sequence converges to 2
D.
Sequence diverges
E.
Sequence converges to –1


3.
Determine the convergence or divergence of the series.

A.
Diverges
B.
Converges
C.
Cannot be determined from the methods in the chapter


4.
Find all values of x for which the series converges. For these values of x, write the sum of the series as a function of x.

A.
B.
C.
D.
E.


5.
Find all values of x for which the series converges. For these values of x, write the sum of the series as a function of x.

A.
B.
C.
D.
E.
Series diverges for all x


6.
Use the Integral Test to determine the convergence or divergence of the series.

A.
Converges
B.
Diverges
C.
Integral Test inconclusive


7.
Determine the convergence or divergence of the series.

A.
Diverges
B.
Converges
C.
Inconclusive


8.
Determine the convergence or divergence of the series.

A.
Converges
B.
Diverges
C.
Inconclusive


9.
Use the Direct Comparison Test (if possible) to determine whether the series converges or diverges.
A.
B.
C.
Direct Comparison Test does not apply


10.
Use the Direct Comparison Test (if possible) to determine whether the series converges or diverges.
A.
B.
C.
Direct Comparison Test does not apply


11.
Use the Limit Comparison Test (if possible) to determine whether the series converges or diverges.
A.
B.
C.
Limit Comparison Test does not apply


12.
Which of the series below should be used in the Limit Comparison Test to determine
whether the series converges or diverges? Does this series converge or diverge?
A.
compare to ; converges
B.
compare to ; diverges
C.
compare to ;
D.
compare to ; converges
E.
compare to ; diverges


Theorem 9.14 (Alternating Series Test):
   Let The alternating series
       and
   converge if the following two conditions are met
   1.       2. for all n.



13.
Determine whether the series converges absolutely, converges conditionally, or diverges.
A.
B.
C.
converges conditionally


14.
Use the Ratio Test to determine the convergence or divergence of the series.

A.
Ratio Test is inconclusive
B.
Diverges
C.
Converges


15.
Use the Root Test to determine the convergence or divergence of the series.

A.
Diverges
B.
Root Test is inconclusive
C.
Converges


16.
Determine the convergence or divergence of the series using any appropriate test from this chapter. Identify the test used.

A.
Converges; p-series
B.
Diverges; p-series
C.
Converges; Integral Test
D.
Diverges; Ratio Test
E.
Both A and C
F.
Both B and D


17.
Determine the convergence or divergence of the series using any appropriate test from this chapter. Identify the test used.

A.
Diverges; p-series
B.
Converges; p-series
C.
Converges; Ratio Test
D.
Diverges; Integral Test
E.
Both A and C
F.
Both B and D


18.
Find the Maclaurin polynomial of degree 3 for the function.

A.
B.
C.
D.
E.


19.
Find the third degree Taylor polynomial centered at c = 4 for the function.

A.
B.
C.
D.
E.


20.
Find the radius of convergence of the power series.

A.
B.
10
C.
100
D.
E.


21.
Use the power series



to determine a power series, centered at 0, for the function. Identify the interval of convergence.

A.
B.
C.
D.
E.


22.
Find a geometric power series for the function centered at 0, (i) by the technique shown in Examples 1 and 2 and (ii) by long division.

A.
B.
C.
D.
E.
None of the above



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