1) What is the goal of mathematical induction? a) Proving that the statement is true for all natural numbers. b) Inducing a mathematical equation is true for a single value. c) Proving that the statement is true for a set of natural numbers. d) To assume the statement is true. 2) What are the steps in mathematical induction? a) Base case and inductive step b) Statement proof and induction step c) Initial case and stepping stairs d) Foundation case and first step 3) How is the inductive hypothesis used? a) To substitute a part of the statement in the inductive step. b) To substitute a part of the statement. c) To substitute a part of the statement in the base case. d) To substitute a part of the statement in the initial case. 4) What is the base case? a) Prove that the statement holds for natural numbers. b) Prove that the statement holds for 1. c) Prove that the statements holds for any one real number. d) Prove that the statement holds for n. 5) What is the inductive step? a) Prove that the statement holds true for the next term (k+1). b) Prove that the statement holds true for the next term (k). c) Prove that the statement holds true for the previous term (k-1) d) Prove that the statement holds true for infinity. 6) What is the difference of strong induction and weak (regular) induction? a) Strong induction involves proving the base case and the induction step separately. b) Strong induction assumes the statement is true for n = k and proves it for n = k + 1 c) Strong induction assumes the statement is true for all values up to n = k to prove it for n = k + 1. d) Strong induction does not require a base case. 7) Which one is the inductive hypothesis? a) b) c) d) 8) How to do the first step in proving this statement with mathematical induction? a) b) c) d) 9) How to do the second step in proving this statement with mathematical induction? a) b) c) d) 10) How is the induction hypothesis used to prove this statement? a) b) c) d) 11) How to do the base case in this statement? a) Check if p(n) is true. b) Check if p(infinity) is true. c) Check if p(1) is true. d) Check if p(k) is true. 12) Which one is the inductive hypothesis in this statement? a) b) c) d) 13) How to do the base case if the statement is p(n) : 3^n - 1 is divisible by 2, where n is greater than 1. a) Check if p(0) is true. b) Check if p(1) is true. c) Check if p(2) is true. d) Check if p(k) is true. 14) For the statement p(n) : 3n - 1 = n(n+1), where n is greater than 5, how to do the first step? a) Check if p(1) is true. b) Check if p(0) is true. c) Check if p(5) is true. d) Check if p(6) is true. 15) What set of numbers works for mathematical induction a) Real numbers b) Natural numbers c) Whole numbers d) Integers

Mathematical Induction Practice Problems

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