Need help for calclus 2 exam.
MATH 201-01 Practice Exam II
1. Find the limit of each sequence if it converges
a.
2
2
3
5
6
n
n
n
a
n
+
+
=
b.n
n
n
n
a
5
4
3
+
=
c.n
n
n
a
n
cos
sin
+
=
d.
!
2
n
a
n
n
=
e.)
1
sin(
n
a
n
=
2. Find the first five terms of the sequence of partial sums of each series
a.
å
¥
=
+
1
1
2
1
n
n
b.å
¥
=
+
-
1
1
2
)
1
(
n
n
n
c.å
¥
=
-
1
1
2
5
n
n
d.å
¥
=
-
2
2
1
1
n
n
3. Determine the convergence of the series
a.
å
¥
=
+
1
2
1
n
n
n
b.)
6
.
0
3
(
0
å
¥
=
-
+
n
n
n
c.å
¥
=
+
1
)
1
ln(
n
n
n
d.å
¥
=
2
ln
1
n
n
n
e.
å
¥
=
+
0
3
1
5
n
n
f.å
¥
=
1
!
2
n
n
g.å
¥
=
1
2
ln
n
n
n
4. Determine the convergence of the series and indicate the test that you use.
a.
å
¥
=
+
-
+
-
1
2
4
2
1
5
1
2
n
n
n
n
n
b.å
¥
=
+
1
)
4
(
5
n
n
n
c.å
¥
=
0
)
01
.
1
(
5
n
n
d.å
¥
=
+
0
5
1
n
n
n
e.
å
¥
=
2
2
)
(ln
1
n
n
n
f.å
¥
=
+
1
4
3
1
n
n
n
g.å
¥
=
+
1
3
1
1
n
n
h.å
¥
=
+
0
2
)
2
(
n
n
n
n
5. Find the sum of the convergent series.
a.
å
¥
=
+
+
0
)
3
)(
1
(
1
n
n
n
b.å
¥
=
÷
ø
ö
ç
è
æ
-
0
3
4
2
3
n
n
n
c.L
+
+
+
000011
.
0
0011
.
0
11
.
0
6. Determine whether each alternating series converges conditionally, absolutely or diverges
a.
å
¥
=
-
-
1
2
1
2
)
1
(
n
n
n
n
b.å
¥
=
+
-
1
2
1
)
1
(
n
n
n
n
c.å
¥
=
+
-
1
2
2
1
)
1
(
n
n
n
n
d.å
¥
=
-
0
!
100
)
1
(
n
n
n
n
e.
å
¥
=
-
2
ln
)
1
(
n
n
n
n
f.å
¥
=
-
1
)
1
cos(
)
1
(
n
n
n
7. Determine the number of terms needed to approximate the value of the convergent alternating series
å
¥
=
-
0
!
2
)
1
(
n
n
n
n
with an error less than 0.00001 and find the approximated value of the series using the sum of this many terms.8. Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.
a. If both
å
å
-
)
(
and
n
n
a
a
converge, thenå
|
|
n
a
converges.b. If
å
n
a
diverges, thenå
|
|
n
a
divergesc. If
å
n
a
andå
n
b
both converge, thenå
n
n
b
a
converges