Math 1210-007
Practice Problems
Fall 2010
Practice Problems - 8/31/10
Using the basic laws of geometry, prove the following properties
1.
2.
3.
The sum of the interior angles of a triangle add to 180 degrees.
 x y 2=x 22xy y 2
The sum of the angles in a regular n-gon (A regular polygon with n sides) is 180 n−2 .
[Hint: break up the polygon into triangles and determine the interior angles of each triangle.]
Prove the following formulas using the Mathematical Induction.
n
n n1
2
4.
∑k =1 k =
5.
∑k =1  2k−1=13572n−1=n 2
6.
∑k =0 2 k=2021222 n=2 n1−1
7.
n
n
n! > 2 n when n≥4 (Recall that 4! = 4⋅3⋅2⋅1 )
[Hint: In step 1 you want to show this works when n = 4]
[Hint: Instead of using a string of equalities to demonstrate this, you will use a string of
inequalities. The proof is simple but it may be challenging to figure out.]