Math 166
Fall 2001
Exam 3
- (15 pt) Determine whether the following sequences converge:
a) 
b) 
where 
is the 
partial sum of the
positive term series 
c) 
- (36 pt) Determine if the following series converge:
a) 
b) 
c) 
d) 
e) 
f) 
- (10
pt) Both series
and 
converge.
a)
Find the smallest 
so that the error of estimating 
with the 
partial sum gives an
error bound less than or equal to .01.
b)
Find the smallest 
so that the error of estimating 
with the 
partial sum gives an
error bound less than or equal to .01.
- (16
pt) Find the center, radius, and interval of convergence of the power
series
- (18
pt) Consider the function
a)
Find a series for 
centered at 
What is its radius of
convergence?
b)
Use your series to show that 
c)
How many terms are necessary so that using the 
partial sum of the
series above to estimate 
gives an error bound of less than .01?
- (15
pt) Consider the functions
and 
a)
Find Maclaurin series for 
and 
b)
Evaluate 
with error less than or equal to 
c)
Evaluate 