Fall 2005 Math 152
courtesy: Amy Austin
(covering sections 10.1, 10.2)
6. Find the sum of the following series. If it diverges,
support your answer.
a.)
a.) an = √
n
n+2
c.)
d.)
b.) an = ln(n) − ln(3n + 1)
(−1)n n
c.) an = 2
n +1
(−1)n n2
n2
ln n
n
a.) a4
b.) the limit of the sequence.
3. Determine whether the following sequences are increasing, decreasing, or non monotonic:
1
a.) an = 5
n
n2 + 4n + 5
b.) an =
n2
ln n
c.) an =
n
d.) an = cos(nπ)
Section 10.2
4. Find the first few partial sums of the series
∞ 1
∞ 1
P
P
. Try to determine whether they
and
2
n=1 n
n=1 n
converge/diverge.
∞
P
n=1
an is a convergent series and
n
is a formula for the nth partial
2n + 3
sum. What is the sum of the series?
sn = 5 +
e.)
f.)
+1
2. Suppose {an } was given to be a convergent se1
quence, a1 = 2, and an+1 =
, find:
3 − an
5. Suppose
1
1
−
n+5 n+6
n
b.)
ln
n+1
n=2
1. Find the limit of the following sequences, if it exists.
If the sequence diverges, state why.
e.) an =
n=1
∞
P
Section 10.1
d.) an =
∞
P
g.)
h.)
∞
P
1
n(n
+ 2)
n=1
n−1
∞
P
n=1
∞
P
2
1
7
n
(−5)
n=1
2
3
∞ (−1)n + 3n
P
n=0
5n
∞ (−1)n 2n
P
n=2
3n+1
∞ (−1)n 32n
P
n=0
i.) 4 +
7n+1
8 16
32
+
+
+ ...
5 25 125