# Exam pm ```BC 3
Sequences and Series Quiz
No Calculators allowed.
Show set-up/method clearly on all problems.
#1.
Name:
Complete (no work necessary):

a
a. An expression of the form
k 1
k
is called an
.
Corresponding to this, we have the sequence {Sn}, which is called the
. The nth term of this sequence is given by Sn =
The sequence {an} is called
If lim(an )  0 then
.
.
.
n 

b. The series
ar
k
converges to
if and only if
&lt;r&lt;
k 1
c. Root Test: If lim 
n 
  L ,
, and

a
, then
k 1
#2 (2 pts each)
Look at the series
k
converges.

n
k 1
k 1
 ak . Let Sn   ak 
n 1
for all n  1. .
n
a. Find a1 , a2 and a3 .

b. Determine whether
a
k 1
k
converges or diverges. If it converges, find the sum.
#3(6 pts each) Determine whether each series converges or diverges. Explain reasoning
carefully and completely.

a.
b.
3n

2
n
n 1 n  2
 2
 1  
 n

n 1

c.
 tan
n 1
n
2
2
1
( n)
#3 (continued) Determine whether each series converges or diverges. Explain reasoning
carefully and completely.
n ! n n

n 1 (2n)!

d.

1
1
approximates
the
value
of

k
k
k 1 k  5
k 1 k  5
with an error less than .001. You need only find the value of n, not S n . Explain your
reasoning clearly.
n
#4(6 pts) Find a value of n such that S n  

#5 (3 pts) Evaluate the sum
3k
5
k 1
k
.
```