Friday, March 1
Clicker Questions
Clicker Question 1
Trying to make a sequence converge
Let {an } be a sequence that we hope converges. Each of these
statements might or might not be true:
I. Every term is larger than the previous one:
a1 < a2 < a3 < · · · .
II. All of the terms are real numbers between 1 and 8.
Which statement(s), if true, would always force {an } to
converge?
A. either one of I or II is enough to make {an } converge
B. I makes {an } converge, regardless of whether II is true
C. II makes {an } converge, regardless of whether I is true
D. nether I nor II makes {an } converge by itself, but together
I and II make {an } converge
E. even I and II together don’t make {an } converge
Clicker Question 2
Almost a geometric series
Calculate
A.
B.
C.
D.
E.
7
9
9
9
9
+
+
+
+
+ ···.
10 100 10,000 1,000,000 100,000,000
87
110
4
5
70
99
1
11
none of the above
From our formula
∞
X
9
7
1 r−1
+
10
100 100
i=1
7
9/100
+
10 1 − 1/100
7
9
=
+
10 100 − 1
7
1
=
+ .
10 11
=