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This quiz focuses on various mathematical concepts including the computation of summations and identification of arithmetic or geometric sequences. It also evaluates the countability of sets such as real numbers, integers, and rational numbers. Additionally, it covers the Fibonacci sequence, requiring participants to state its initial values, describe its recurrence relation, and provide a proof of its countability through mapping to positive integers. Finally, a proof by induction is required for a specified result.
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Quiz 6 3.2 3.3 3.4
Quiz 6, May 27, 3.30-3.45 pm 1) a) Compute the value of the following summations: b) For both sequences indicate whether they are arithmetic or geometric progressions. 2) a) Indicate whether the following sets are countable or uncountable: the real numbers (R), the integers (Z), the rational numbers (Q). b) What is the Fibonacci sequence (i.e. provide the initial values and the recurrence relation. c) Give a short prove or argument that the Fibonacci sequence is countable. 3) Prove the following result by induction:
Quiz 6, Answers 1) a) Compute the value of the following summations: b) For both sequences indicate whether they are arithmetic or geometric progressions. 2) a) Indicate whether the following sets are countable or uncountable: the real numbers (R), the integers (Z), the rational numbers (Q). R = uncountable, Z = countable, Q = countable. b) What is the Fibonacci sequence (i.e. provide the initial values and the recurrence relation. c) Give a short prove or argument that the Fibonacci sequence is countable. You can map it to the positive integers (since it is a sequence: a1, a2, a3,...) 3) Prove the following result by induction: white board
