Problem 1TY: A recursive definition for a sequence consists of a and . Problem 2TY: A recurrence relation is an equation that defines each later term of a sequence by reference to in... Problem 3TY Problem 4TY: To solve a problem recurisively means to divede the proble into smaller subproblems of the same type... Problem 5TY Problem 1ES: Find the first four terms every of the recursively defined sequences in 1-8. ak=2ak1+k , for every... Problem 2ES: Find the first four terms of each of the recursively defined sequences in 1-8. bk=bk1+3k, for every... Problem 3ES: Find the first four terms of each of the recursively defined sequences in 1-8. ck=k(c k1)2 , for... Problem 4ES: Find the first four terms of each of the recursively defined sequences in 1-8. dk=k(d k1)2 , for... Problem 5ES: Find the first four terms of each of the recursively defined equences in 1-8. sk=sk1+2sk2, for every... Problem 6ES: Find the first four terms of each of the recursively defined equences in 1-8. tk=tk1+2tk2. for every... Problem 7ES: Find the first four terms of each of the recursively defined equences in 1-8. uk=kuk1uk2, for every... Problem 8ES: Find the first four terms of each of the recursively defined equences in 1-8. vk=vk1+vk2+1 , for... Problem 9ES Problem 10ES: Let b0,b1,b2... be defined by the formula bn=4n, for every integer n0 . Show that this sequence... Problem 11ES: Let c0,c1,c2,... be defined by the formula cn=2n1 for every integer n0. Show that this sequence... Problem 12ES: Let S0,S1,S2,... be defined by the formula Sn=( 1)nn! for every integer n0 . Show that this sequence... Problem 13ES Problem 14ES: Let d0,d1,d2,... be defined by the formula dn=3n2n for every integer n0 . Show that this sequence... Problem 15ES: For the sequence of Catalan numbers defined in Example 5.6.4, prove that for each integer n1,... Problem 16ES: Use the recurrence relation and values for the Tower of Hanoi sequence m1,m2,m3,... discussed in... Problem 17ES: Tower of Hanoi with Adjacency Requirement: Suppose that in addition to the requirement that they... Problem 18ES Problem 19ES: Four-Pole Tower of Hanoi: Suppose that the Tower of Hanoi problems has four poles in a row instead... Problem 20ES: Tower of Hanoi Poles in a Curie: Suppose that instead of being lined up in a row, the three polesfor... Problem 21ES: Double Tower of Hanoi: In this variation of the Tower of Hanoi there are three poles in a row and 2n... Problem 22ES: Fibonacci Variation: A single pair of rabbits (male and female) is born at the beginning of a year.... Problem 23ES: Fibonacci Variation: A single pair of rabbits (male and female) is born at the beginning of ayear.... Problem 24ES: In 24-34, Fa,F1,F2,...is the Fibonacci sequence. Use the recurrence relation and values for... Problem 25ES: In 24-34, Fa,F1,F2,...is the Fibonacci sequence. The Fibonacci sequence satisfies the recurrence... Problem 26ES: In 24—34, F0,F1,F2,.... is the Fibonacci sequence. 26. Prove that Fk=3Fk3+2Fk4for every integer k4 . Problem 27ES Problem 28ES Problem 29ES Problem 30ES Problem 31ES: In 24-34, Fa,F1,F2,...is the Fibonacci sequence. Use strong mathematical induction to prove that... Problem 32ES: In 24-34, Fa,F1,F2,...is the Fibonacci sequence. Prove that for each integer n0 , gcd... Problem 33ES Problem 34ES Problem 35ES Problem 36ES Problem 37ES Problem 38ES: Compound Interest: Suppose a certain amount of money is deposited in an account paying 3% annual... Problem 39ES: With each step you take when climbing a staircase, you can move up either one stair or two stairs.... Problem 40ES: A set of blocks contains blocks of heights 1, 2, and 4 centimeters. Imagine constructing towers by... Problem 41ES Problem 42ES Problem 43ES Problem 44ES Problem 45ES Problem 46ES Problem 47ES format_list_bulleted