Consider the formula where n is an integer and 3, = (2)(+3) =3 2

Expand the left hand side of the formula (rewrite without the Sigma notation)

Prove the formula by using mathematical induction.

3. Define a sequence 1, 2, 3, ... : 1 = 1, 2 = 3, = 1 + 2 for all integers 3

a. Use strong mathematical induction to prove that < (7) 1 4

i. Hint, treat the inequality as you would an equality, and only change the inequality if multiplying by negative.

4. Given the recurrence relation = 41 32 999 h 0 = 5 1 = 7.