MATH 101 Quiz #6 (v.A2)
Last Name:
Friday, April 1
First Name:
Grade:
Student-No:
Section:
Very short answer question
P
1. 1 mark Suppose you wanted to use the Limit Comparison Test on the series ∞
n=0 an where
n +2
an = 53n +n
. Write down a sequence {bn } such that limn→∞ abnn exists and is nonzero. (You don’t
have to carry out the Limit Comparison Test; just write the formula for the bn .)
Answer:
Short answer questions—you must show your work
P
2
(−1)n−1
2. 2 marks It is known that ∞
= π12 (you don’t have to show this). Find N so that
n=1
n2
2
SN , the N th partial sum of the series, satisfies | π12 − SN | ≤ 35−2 . Be sure to say why your
method can be applied to this particular series.
Answer:
3. 2 marks Does the series
∞
X
n sin n
n=5
Explain your answer.
n3 − 1
converge conditionally, converge absolutely, or diverge?
Long answer question—you must show your work
4. 5 marks Find the radius of convergence and interval of convergence of the series
n
∞
X
(−1)n x + 3
.
n
+
1
3
n=0