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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 22xy 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 n1 2 4. ∑k =1 k = 5. ∑k =1 2k−1=13572n−1=n 2 6. ∑k =0 2 k=2021222 n=2 n1−1 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.]