Math
166
Fall 2000
Exam 3
1.
(15
pt) Determine if the following sequences converge or diverge, if the sequence
converges, then find the limit:
a) 
b) 
c) 
where 
2.
(12
pt) Consider the sequence 
where 
is the nth
partial sum of the series 
a)
Find
all values of p for which the
sequence converges (and state why).
b)
Find
all values of p for which the
sequence does not converge to 0 (and state why).
3.
(36
pt) Determine if the following series converge or diverge:
a) 
b) 
c)
d) 
e) 
f) 
4.
(12
pt) For this problem consider the two convergent series 
a)
How
big must you choose n to guarantee that the approximation sn
for the series 
has error less than or equal to .01?
b)
How
big must you choose n to guarantee that the approximation sn
for the series 
has error less than or equal to .01?
5.
(10
pt) Find the center, radius, and interval of convergence of the power series 
6.
(9
pt) Suppose that if you expand the function 
in a power series
about c, 
is equal to its power series on the interval (0,c).
Also assume that 
has a vertical asymptote at 0. Suppose you expand 
in a Taylor series centered at 1. Determine if you can use
this series to estimate the following in general: 
Why or why not?
7.
(8
pt) Evaluate the integral 
with error less than .001.
8.
(8
pt) Find a series for 
about 
What is the radius of convergence of this series?