Math 128
ASSIGNMENT 8
Winter 2009
Submit all problems by
8:20 am
on
Wednesday, March 25
th
in the drop boxes across
from MC4066, or in class depending on your instructor’s preference.
All solutions must be
clearly stated
and
fully justified
.
Comment: This assignment is longer than usual. It is strongly recommended that you start
working on it early.
1. Find the sum of the given geometric series.
a)
∞
n
=0
3
(
-
1
4
)
n
b)
∞
n
=0
π
n
2
3
n
-
1
c)
∞
n
=0
3 + 2
n
3
n
+2
2. Apply the
n
th
Term Test (i.e.
Divergence Test) or the Comparison Test to decide
whether each series converges, converges absolutely, or diverges.
a)
∞
n
=2
n
+ 1
n
-
1
b)
∞
n
=1
sin
nx
2
n
,
x
∈
R
c)
∞
n
=1
2
n
n
3
n
d)
∞
n
=0
1
1 + 3
n
e)
∞
n
=1
1
2
-
1
n
2
f)
∞
n
=0
cos(
n
2
)
π
n
+ 3
3. Determine whether each of the following series converges absolutely or diverges by
comparison to an appropriate
p
-series. (You may use the result of example 2 on page
699 of your text.)
(i)
∞
n
=2
1
√
n
-
1
(ii)
∞
n
=1
(
-
1)
n
n
n
4
+ 2
(iii)
∞
n
=1
arctan 2
n
n
2
4. Apply the integral test to determine whether or not each series converges.
This
preview
has intentionally blurred sections.
Sign up to view the full version.

This is the end of the preview.
Sign up
to
access the rest of the document.
- Spring '10
- Zuberman
- Math, Mathematical Series, nth term test, single leaning pile, MC4066, convergent alternating series
-
Click to edit the document details