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