ECE 302, Midterm #1
6:307:30pm Thursday, February 5, 2009, EE 170,
1. Enter your name, student ID number, email address, and signature in the space
provided on this page,
NOW!
2. This is a closed book exam.
3. This exam contains multiple choice questions and workout questions. For multiple
choice questions, there is no need to justify your answers.
You have one hour to
complete it. The students are suggested not spending too much time on a single
question, and working on those that you know how to solve.
4. There are 13 pages in the exam booklet. Use the back of each page for rough work.
5. Neither calculators nor help sheets are allowed.
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Question 1:
[15%]
Consider a sequence
p
k
such that for any integer
k
, we have
p
k
=
3

k

2
.
Let
F
(
m
) =
∑
m
k
=
∞
p
k
.
1. [8%] Find the expression of
F
(
m
) for
m
≤
0.
2. [7%] Find the value of
∑
∞
k
=
∞
p
k
e
0
.
1
k
.
Hint: The infinite sum of a geometric series is as follows.
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 Spring '08
 GELFAND
 Probability theory, A Closed Book

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