BC 3
Sequences and Series Quiz
Name:
No Calculators allowed.
Show set-up/method clearly on all problems unless otherwise specified.
#1.(9 pts) Determine whether each sequence converges. If so, write the limit. If not,
write “diverges”. No work necessary.
a.
an =
n3
n  n
3
 n  3
b. bn =Ln 
 n 
c. cn 
3n3  3n
n 3  2n 2  1
1
d. d n  n cos  
n
#2(5 pts) Find an expression for the sequence of partial sums, S n , for the series

 2k  1 
 Ln  2k  1  . Use this to determine whether the series converges or diverges. If the
k 3
series converges, find the value.
#3(9 pts) Determine whether each series is geometric. If it is, either determine its sum or
state that it diverges. For those geometric series containing an x, state clearly the limits on
the variable x for which the series converges.
a.
3 3
3
 

5 10 20
b.
x

x 2 x3 x 4
  
3 9 27
3

5  2k
 (1)k 1
xk

3k 1
c. ( x  3)  ( x  3)3  ( x  3)6  ( x  3)10 
 ( x  3)
k ( k 1)
2

#4(5 pts) Find an explicit formula for the sequence:
2
3
4
5
1 2 3 4
0,   ,   ,   ,   , ........................
2 3 4 5
Determine whether this sequence converges. If so, find the limit showing all work. If
not, explain.