Math 1Z04 Test #3
(Version 4)
November 20th, 2009
Name
:___________________________________________
(Last Name)
(First Name)
Student Number:
_____________________
This test consists of 18 multiple choice questions worth 1 mark each (no part marks), and 1
question worth 1 mark on proper computer card filling.
Questions must be answered on the
COMPUTER CARD with an HB PENCIL.
Marks will not be deducted for wrong answers (i.e.,
there is no penalty for guessing).
You are responsible for ensuring that your copy of the test is
complete.
Bring any discrepancy to the attention of the invigilator.
Calculators are NOT
allowed.
1.
Which of the following series converge?
(i)
(ii)
8œ"
8œ"
∞∞
$
8
8
8#
#
8"
$"
(a)
(b)
(c)
(d)
(ii) only
(i) only
(i) and (ii)
neither
2.
Suppose that we were to use Mathematial Induction to show that
3œ
8
3"
8
1
#œ
#
"
.
Which of the following would be the second step?
(a)
Assume that
, and show that
3œ"
3œ"
55
"
38
3
"8
#œ#
# œ#"
(b)
Assume that
, and show that
3œ"
3œ"
5"
5
3"
5
3"
5"
#
"
#
"
(c)
Assume that
, and show that
3œ"
3œ"
5"
5
3"
5"
3"
5
"
#
"
(d)
Assume that
, and show that
3œ"
3œ"
"
3"
5
3"
5"
#
"
"
(e)
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 Spring '08
 CHILDS
 Following, Þ, following series converge, Mathematial Induction

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