MATH 101 Quiz #6 (v.A1)
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
an
an = 23n+n
.
Write
down
a
sequence
{b
}
such
that
lim
exists
and
is
nonzero.
(You don’t
n
n→∞ bn
+1
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 | ≤ 10−6 . Be sure to say why your
method can be applied to this particular series.
Answer:
3. 2 marks Does the series
∞ √
X
n cos n
n=5
Explain your answer.
n2 − 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 + 2
.
n
+
1
2
n=0