Math
166
Summer 2002
Exam 3
- (18 pt) Determine if
the following sequences converge or diverge.
a) 
b) 
c) 
where 
is the 
partial sum of a positive term series.
- (36 pt) Determine if
the following series converge.
a) 
b) 
c) 
d) 
e) 
f) 
- (15 pt) Suppose that you have an infinite series of the form
with partial sums given by 
a)
Suppose
that you find that 
Does the series
converge? Why or why not.
b)
Suppose
that you find that 
Does the series
converge? Why or why not.
c)
In
both cases above, compute 
and justify your
answer.
- (10 pt) Find the center, radius and interval of convergence of the
power series
- (8 pt) Find a series for
about the point 
What is the
radius of convergence of this series? - (15 pt) Consider the function
a)
Show
that 
.
b)
Use
this to show that 
c)
How
many terms do you need to guarantee that the approximation 
has error less than or equal to .001?
7. (8 pt) Evaluate 
with error less that
or equal to 