The document discusses inductive reasoning and how it can be used to find patterns in sequences to make conjectures. It provides examples of using inductive reasoning to find the next terms in sequences and make conjectures about sums or patterns. It also discusses what a counterexample is and how it can disprove a conjecture. The homework assigned is to complete problems 2-46 even on pages 6-7.
1. Find a pattern for each sequence. Use the pattern to show the next 2 terms. 5, 10, 20, 40, … 1, 2, 6, 24, 120, … 1, 3, 7, 13, 21, … M, V, E, M, … 80, 160 720, 5040 31, 43 J, S
8. What is a conjecture? A conclusion you reach using inductive reasoning.
9. Example: Using Inductive Reasoning. Make a conjecture about the sum of the first 30 odd numbers. Find the first few sums. Notice that each sum is a perfect square. 1 = 1 = 1 + 3 = 4 = 1 +3 + 5 = 9 = Using inductive reasoning you can conclude that the sum of the first 30 odd numbers is 30 squared, or 900.
10. What is a counterexample? An example for which the conjecture is false. You can prove that a conjecture is false by finding one counterexample.
11. Example: Testing a conjecture and finding a counterexample. If it is cloudy, then it is raining. It is cloudy and it is not raining.
