3.1. Observe that 1 = 1 1-4 = -(1+ 2) 1– 4+9 = 1+2+3 1– 4+9–16 = -(1+2+3+4) 1-4+9– 16+25 = 1+2+3+4+5. Guess a general formula and prove it by mathematical induction. 3.2. You have two parents, four grandparents, eight great-grandparents, and so forth. 3.2.1. If all your ancestors were distinct, what would be the total number of your ancestors for the past 40 generations (counting your parents' generation as number one)? (Hint: Use the formula for the sum of a geometric sequence.) 3.2.2. Assuming that each generation represents 25 years, how long is 40 generations? 3.2.3. The total number of people who have ever lived is approximately 10 billion, which equals 1010 people. Compare this fact with the answer to part (a). What can you deduce?

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.