Math
161
Spring 2000
Exam 3
1.
(30
pt) Determine if the following sequences converge or diverge:
a) 
b) 
c) 
(hint: if 
then 
).
d) 
(hint: look at problem
2 e)) e) 
2.
(30
pt) Determine if the following series converge conditionally, converge
absolutely, or diverge:
a) 
b) 
c) 
d) 
(
). e) 
3.
(12
pt) Consider the positive term series
with sequence of
partial sums given by 
.
a)
Assume
that 
diverges. Determine if the sequence 
converges or tell why there is not enough information given
to determine the answer.
b)
Assume
that the sequence 
converges, determine
if the sequence 
converges or explain
why there is not enough information given.
4.
(12
pt) It can be shown by the integral test that the series 
converges. How many terms do we need to use to ensure that
our partial sum estimate has error less than or equal to .000025?
5.
(12
pt) Consider the function 
.
a)
Find
a power series representation for 
b)
What
is the Taylor polynomial 
c)
Use
to estimate 
and give an estimate of your error.
6.
(12
pt) Find the Maclaurin series of the function 
. Can you use this series to estimate 
Why or why not?
7.
(12
pt) Find the center, radius and interval of convergence of the power series
