Question 1 Our first section of this topic deals with a specific proof technique of mathematical induction. This is an incredibly powerful tool. Fill in the words below to Not yet answered complete the definition. Points out of 2.00 P Flag question is a mathematical technique which is used to a statement, a formula or a theorem is true for every number. The technique involves two steps to prove a statement, as stated below - Step 1 - It proves that a statement is true for the initial value. Step 2 - It proves that if the statement is true for the nth iteration (or number n), then it is for (n+ 1)th iteration ( or number n+ 1). Next pageQuestion 2 Put the following steps of the proof in order. Not yet answered Points out of We have to prove that 3* - 1 is also a multiple of 2 2.00 Prove 3" - 1 is a multiple of 2 for n = 1, 2, ... P Flag question Hence, 3*-1 is a multiple of 2. The first part (2 x 3*) is certain to be a multiple of 2 and the second part (3* - 1) is also true as our previous assumption. So, it is proved that 3"-1 is a multiple of 2. Step 1: For n=1, 31 - 1 =3 - 1 = 2 which is a multiple of 2 3ktl _ 1 = 3 x 3* - 1 = (2 x 3*) + (3* - 1) Step 2: Let us assume the statement 3" - 1is true for some n=k Hence, from our assumption, 3" - 1 is a multiple of 2 Previous page Next pageQuestion 5 True or False: The following relation is an example of a linear recurrence relation Not yet Fn = 3Fn1 + Fn-4 given initial values aq = a2 = a3 = a4 = 1 answered Points out of 2.00 Select one: P Flag question O True O FalseQuestion 4 An example of a recurrence relation is the Fibonacci sequence. The relation is given by Fr = Fn-1 + Fn-2 Not yet Here is the start of this sequence: answered Points out of 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, (next?) 2.00 Provide below one of the numbers that will be added to make the (next?) number in the sequence. P Flag question Answer: Previous pageQuestion 6 True or False: The following relation is an example of a linear recurrence relation Not yet answered Fn = 3(Fn-1)( Fn-4) given initial values a, = a2 = a3 = a4 = 1 Points out of 2.00 Flag question Select one: O True O FalseTime left 0:58:10 Question 3 Our next section has to do with recurrence relations. Fill in the definition below. Not yet answered A relation is an that recursively defines a where the next term is a function of the terms. Points out of 2.00 Expressing F as some combination of Fi with in recurrence P Flag question equation sequence previous summation Previous page Next page