MATH 311W Quiz: Math 311w quiz02
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Instructions: clearly answer each of the questions below. Remember to check the back side if blank, you can use it for scrap work. Show your work and any formulas you employ. Math 311, quiz 2: state the binomial theorem. Answer:the binomial theorem says that for any positive integer n, and any real number x, (1 + x)n = n. Answer: two numbers are relatively prime when there is no integer greater than 1 that evenly divides both: prove that for all positive integers n, 3|5n 2n. Answer: i will prove this to you using regular induction. If n = 1, then 5n 2n = 5 2 = 3 and 3|3, so for our base case, if n = 1, then 3|5n 2n. Now, let"s assume for some integer k, 3|5k 2k. = 3(5k) + 2(5k 2k). from the de nition of divisibility, 3|3.
