Name: WA 4, p. 1 Name: University ID: Thomas Edison State University Calculus II (MAT-232) Section no.: Semester and year: Written Assignment 4 Answer all assigned exercises, and show all work. Each...

Name:
    WA 4, p. 1
Name:
University ID:
Thomas Edison State University
Calculus II (MAT-232)
Section no.:
Semester and year:
Written Assignment 4
Answer all assigned exercises, and show all work. Each exercise is worth 4 points.
Section 8.1
2. Write out the terms 126
,,,
aaa
K
of the sequence.
3
4
n
a
n
=
+
8. (a) Find the limit of the sequence, (b) use the definition to show that the sequence converges, and (c) plot the sequence on a calculator or CAS.
    21
n
n
a
n
+
=
12. Determine whether the sequence converges or diverges.

    3
3
51
21
n
n
a
n
-
=
+
18. Determine whether the sequence converges or diverges.

    cos
n
an
p
=
20. Determine whether the sequence converges or diverges.
    
    cos
n
n
n
a
e
=
    
Section 8.2
4. Determine whether the series converges or diverges. For convergent series, find the sum of the series.
    
    0
1
4
2
k
k
¥
=
æö
ç÷
èø
å
8. Determine whether the series converges or diverges. For convergent series, find the sum of the series.
    
    1
4
2
k
k
k
¥
=
+
å
10. Determine whether the series converges or diverges. For convergent series, find the sum of the series.
    
    1
9
(3)
k
kk
¥
=
+
å
20. Determine whether the series converges or diverges. For convergent series, find the sum of the series.
    
    2
11
4
k
k
k
¥
=
æö
-
ç÷
èø
å
28. Determine all values of c such that the series converges.
    
    0
2
1
k
ck
¥
=
+
å
Section 8.3
4. Determine convergence or divergence of the series.
8
4
24
k
k
¥
=
+
å
    
2
6
4
(24)
k
k
¥
=
+
å
    
10. Determine convergence or divergence of the series.
3
0
4
1
k
k
¥
=
+
å
2
5
0
1
1
k
k
k
¥
=
+
+
å
    
    
14. Determine convergence or divergence of the series.
4
52
4
21
31
k
kk
kk
¥
=
+-
++
å
    
3
42
6
23
24
k
kk
kk
¥
=
++
++
å
    
26. Estimate the e
or in using the indicated partial sum n
S
to approximate the sum of the series.
    100
2
1
4
,
k
S
k
¥
=
å
28. Estimate the e
or in using the indicated partial sum n
S
to approximate the sum of the series.
    80
2
1
2
,
1
k
S
k
¥
=
+
å
Section 8.4
2. Determine whether the series is convergent or divergent.
2
1
2
(1)
k
k
k
¥
=
-
å
            
4. Determine whether the series is convergent or divergent.
2
1
1
(1)
1
k
k
k
k
¥
+
=
-
+
å
            
    
10. Determine whether the series is convergent or divergent.
1
2
(1)
4
k
k
k
k
¥
=
+
-
å
    

16. Determine whether the series is convergent or divergent.
1
3
!
(1)
3
k
k
k
k
¥
+
=
-
å
18. Determine whether the series is convergent or divergent.
2
4
3
4
22
k
k
kk
¥
=
++
å
Section 8.5
2. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
0
6
(1)
!
k
k
k
¥
=
-
å
            
6. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
2
1
1
1
(1)
k
k
k
k
¥
+
=
+
-
å
            
    
10. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
1
3
4
(1)
21
k
k
k
¥
+
=
-
+
å
    

18. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
1
3
2
(1)
1
k
k
k
k
¥
+
=
-
+
å
32. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
8
2
3
k
k
k
¥
=
å
    
    

Name:
Name:
University ID:
Thomas Edison State University
Calculus II (MAT-232)
Section no.:
Semester and year:
Written Assignment 4
Answer all assigned exercises, and show all work. Each exercise is worth 4 points.
Section 8.1
2. Write out the terms of the sequence.
8. (a) Find the limit of the sequence, (b) use the definition to show that the sequence converges, and (c) plot the sequence on a calculator or CAS.
    
12. Determine whether the sequence converges or diverges.

    
18. Determine whether the sequence converges or diverges.

    
20. Determine whether the sequence converges or diverges.
    
    
    
Section 8.2
4. Determine whether the series converges or diverges. For convergent series, find the sum of the series.
    
    
8. Determine whether the series converges or diverges. For convergent series, find the sum of the series.
    
    
10. Determine whether the series converges or diverges. For convergent series, find the sum of the series.
    
    
20. Determine whether the series converges or diverges. For convergent series, find the sum of the series.
    
    
28. Determine all values of c such that the series converges.
    
    
Section 8.3
4. Determine convergence or divergence of the series.
(a)
(b)
10. Determine convergence or divergence of the series.
(a)
(b)
    
14. Determine convergence or divergence of the series.
(a)
    
(b)
26. Estimate the e
or in using the indicated partial sum to approximate the sum of the series.
    
28. Estimate the e
or in using the indicated partial sum to approximate the sum of the series.
    
Section 8.4
2. Determine whether the series is convergent or divergent.
            
4. Determine whether the series is convergent or divergent.
            
    
10. Determine whether the series is convergent or divergent.
    

16. Determine whether the series is convergent or divergent.
18. Determine whether the series is convergent or divergent.
Section 8.5
2. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
            
6. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
            
    
10. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
    

18. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
32. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
    
    
    WA 4, p. 1
21
n
n
a
n
+
=
3
3
51
21
n
n
a
n
-
=
+
cos
n
an
p
=
cos
n
n
n
a
e
=
0
1
4
2
k
k
¥
=
æö
ç÷
èø
å
1
4
2
k
k
k
¥
=
+
å
1
9
(3)
k
kk
¥
=
+
å
2
11
4
k
k
k
¥
=
æö
-
ç÷
èø
å
0
2
1
k
ck
¥
=
+
å
8
4
24
k
k
¥
=
+
å
2
6
4
(24)
k
k
¥
=
+
å
3
0
4
1
k
k
¥
=
+
å
2
5
0
1
1
k
k
k
¥
=
+
+
å
4
52
4
21
31
k
kk
kk
¥
=
+-
++
å
3
42
6
23
24
k
kk
kk
¥
=
++
++
å
n
S
100
2
1
4
,
k
S
k
¥
=
å
80
2
1
2
,
1
k
S
k
¥
=
+
å
2
1
2
(1)
k
k
k
¥
=
-
å
2
1
1
(1)
1
k
k
k
k
¥
+
=
-
+
å
1
2
(1)
4
k
k
k
k
¥
=
+
-
å
1
3
!
(1)
3
k
k
k
k
¥
+
=
-
å
2
4
3
4
22
k
k
kk
¥
=
++
å
0
6
(1)
!
k
k
k
¥
=
-
å
2
1
1
1
(1)
k
k
k
k
¥
+
=
+
-
å
1
3
4
(1)
21
k
k
k
¥
+
=
-
+
å
1
3
2
(1)
1
k
k
k
k
¥
+
=
-
+
å
8
2
3
k
k
k
¥
=
å
126
,,,
aaa
K
3
4
n
a
n
=
+