Math 172
Quiz 9
Name:
29 Mar 2016
Show Appropriate Work
Point Values in boxes .
1. 2 Please indicate True or F false.
(a) T / F : If an → 0 as n → ∞, the series
P
an converges.
P
(b) T / F : If an → 0 as n → ∞, the series
an diverges.
P
P
(c) T / F : If an < bn and
bn converges, then
an converges.
P
P
(d) T / F : If 0 < an < bn and
bn diverges, then
an diverges.
2. 4 For the following series, specify what series you would compare each to (either direct or
limit comparison) and based on your comparison, decide if it converges or diverges. No formal
justification is needed.
∞ √ 2
X
n +1
(a)
compare to
so it converges / diverges
3
n + 4n
n=2
(b)
∞
X
n=2
(c)
so it converges / diverges
1
√
+ n
compare to
so it converges / diverges
n3 + 3
n2 + n
compare to
so it converges / diverges
∞
X
n=2
(d)
3
√
compare to
2n
∞
X
n=2
n2
n
√
3. 4 Use the Direct Comparison Test to show the following series converges.
∞
X
n=4
n
n3 + 7