Let (a) Show that (b) Prove, by mathematical induction, that An for n 1c 0 1 1 1 d . A 1

InEqualities: 9/2/16 -Less than: Less than or equal to Greater than Greater than or equal to A**B A≥B Transitivity: -If A 0 - D-B>0 - Therefore (D+C) – (A+B) >0 - Therefore D+C > A+B Mult. Of Inequalities: - If A>B… If C>0 AC>BC -3>-6 A=1, B=2, C= -3 Mult. Inverse: - Given a number ,X, the inverse is what the mult. X to get a product of 1. - -2/3 -> -3/2 - Find all numbers X, such that… X-8/X-4 < 3 X-4/1 × X-8/X-4 < 3(X-4) X-8 < 3(X-4) Case 1: X-4 > 0 Case 2: X-4 < 0 X > 4 X < 4 X-8 < 3(X-4) X-8 > 3(X-4) X-8 < 3X-12 X-8 > 3X-12 -8 < 2X-12 -8 > 2X-12 4 < 2X 4 > 2X 2 < X 2 > X Solution: X > 4 & X < 2 Additive inverse of Inequalities: - If A -B**