Announcements
WeBWorK #9 is now open
Due Wednesday at 9pm
Covers material from “Week 9”—see syllabus online
Solutions to (all versions of) Quiz #4 are online
Pick up your quiz papers in the Math Learning Centre
Quiz #5 will take place here on Friday, March 18 (second half of class time)
Covers material from “Week 8” and “Week 9”
You must bring your student ID to class on every quiz day
You must take the quiz in the section you’re registered in

Monday, March 14

Practicing the Limit Comparison Test
Determine the convergence or divergence of these two series:
I .
∞
X n = 7
2 n
1
− 100
II .
∞
X n = 1
√
3
1
4 n 5 + 6
A.
I.
diverges but
II.
converges
B.
I.
converges but II.
diverges
C.
both I.
and II.
diverge
D.
both I.
and II.
converge
Series to compare to lim n →∞
2
− n
I.
lim n →∞ 1 / ( 2 n − 100 )
1 − 100 · 2
− n geometric series
=
=
P
∞ n = 7
1 , and the
2
− n converges.
II.
lim n →∞ lim n →∞
P
∞ p n = 1
3 n
4 n
− 5 / 3
1 /
√
3
4 n 5
+ 6 n
− 5
+ 6
√
3
=
=
4 , and the p -series
− 5 / 3 converges.

The Alternating Series Test
Which of the following series can the Alternating Series Test be applied to?
A.
1 +
1
2
−
∞
X
B.
1 n 3 / 2 n = 1
1
3
C.
D.
+
1
4
+
1
5
−
∞
X
( − 1 ) n
1 + cos n n n = 1
∞
X
( − 1 ) n
1
+
1
2 n n = 1
1
6
+
1
7
+
1
8
− 1
9
+ · · ·
E.
none of the above
Reasons
A is not alternating in the correct way
B is not alternating at all
C does not have a decreasing sequence
D does not have a summand that tends to 0

I love to count
How many of these objects converge?
the sequence the series
∞
X
1
√ n n = 1
1
√ n the sequence ( − 1 ) n
1
√ n the series
∞
X
( − 1 ) n
1
√ n n = 1
A.
0
B.
1
C.
2
D.
3
E.
4
Which ones?
The two sequences both converge to 0 (the second one using a mini-Squeeze Theorem argument). The first series is a p -series with p =
1
2
, so diverges. The second series passes the Alternating Series Test, so converges.

Monday, March 14
Take care of your physical self!
Get enough sleep. (At least most of the time!)
Eat healthy food. (At least most of the time!)
Drink lots of water.
Get frequent exercise. (At least mild exercise.)
Moderate your intake of caffeine, alcohol, other substances. . . .
UR BRAIN WORKS BETTER WHEN UR BODY IS HEALTHY