Name:
Math 100 : Problem Solving
Midterm Exam
Instructor: Ciprian Manolescu
You have 50 minutes.
Each problem is worth 10 points.
No books, notes or calculators are allowed.
1. Let Fn be the Fibonacci numbers, dened by F0 = 0, F1 = 1, and Fn = Fn1 + Fn2
f
Name:
Math 100 : Problem Solving
Midterm Exam
Instructor: Ciprian Manolescu
You have 50 minutes.
Each problem is worth 10 points.
No books, notes or calculators are allowed.
1. Let Fn be the Fibonacci numbers, dened by F0 = 0, F1 = 1, and Fn = Fn1 + Fn2
f
Name:
Math 100 : Quiz
October 3, 2013
You have 25 minutes. No books, notes or calculators are allowed.
1. Prove by induction on n that
2 4 6 (2n)
> n+1
1 3 5 (2n 1)
for any n 1.
2. Show that among any 9 points inside a 10 20 rectangle, we can nd two that
Name:
Math 100 : Problem Solving
Final Exam
Instructor: Ciprian Manolescu
You have 180 minutes.
Each problem is worth 10 points.
No books, notes or calculators are allowed.
1. Prove by induction on n 1 that
2n 1
2n 2 +
2n 3 +
3
2+
1>
n
.
2
2. (a) Find th
Name:
Math 100 : Problem Solving
Final Exam
Instructor: Ciprian Manolescu
You have 180 minutes.
Each problem is worth 10 points.
No books, notes or calculators are allowed.
1. Thirty bees are ying inside a cube of side length 1. Show that at any given tim
Name:
Math 100 : Problem Solving
Midterm Exam
Instructor: Ciprian Manolescu
You have 50 minutes.
Each problem is worth 10 points.
No books, notes or calculators are allowed.
1. Let x1 , x2 , . . . , xn 1. Prove by induction on n that
(1 + x1 )(1 + x2 ) (1
Name:
Math 100 : Problem Solving
Midterm Exam
Instructor: Ciprian Manolescu
You have 50 minutes.
Each problem is worth 10 points.
No books, notes or calculators are allowed.
1. Let x1 , x2 , . . . , xn 1. Prove by induction on n that
(1 + x1 )(1 + x2 ) (1