342 8 Sequences and Series is given in two parts: if a Sn =I+ nc for V n E N; 1, if a + 1, C Sn = a"A+ 1 for Vn E N. a When a = 1, any particular solution is obtained by determining a specific, numerical value for I. In fact, a particular solution is determined by a specific, numerical value J for any (particular) entry, S;. Solving the equation J =I+ jc for I, I = J – jc. // since S; = I+ jc // where So = I we get // One particular “particular solution" has I = 0. When a + 1, any particular solution is obtained by determining a specific, numerical value for A; if the starting value I is given, then A = I – In fact, 1 - a a particular solution is determined by a specific, numerical value J for any (particular) entry, S;. Solving the equation J = Aa + for A, 1 - a 1 A = aj we get // But what if a = 0? 1 - // One particular “particular solution" has A = 0. Example 8.2.1: The Towers of Hanoi The recurrence equation for the number of moves in the Towers of Hanoi problem is a first-order linear recurrence equation: Tn = 2Tn-1+1. C 1 Here a =2 and c = 1, so 1 = -1, and any sequence T that satisfies — а 1 this RE is given by the formula Tn = 2" [1 – (-1)] +(-1) = 2" [I+ 1] – 1.

342 8 Sequences and Series is given in two parts: if a Sn =I+ nc for V n E N; 1, if a + 1, C Sn = a"A+ 1 for Vn E N. a When a = 1, any particular solution is obtained by determining a specific, numerical value for I. In fact, a particular solution is determined by a specific, numerical value J for any (particular) entry, S;. Solving the equation J =I+ jc for I, I = J – jc. // since S; = I+ jc // where So = I we get // One particular “particular solution" has I = 0. When a + 1, any particular solution is obtained by determining a specific, numerical value for A; if the starting value I is given, then A = I – In fact, 1 - a a particular solution is determined by a specific, numerical value J for any (particular) entry, S;. Solving the equation J = Aa + for A, 1 - a 1 A = aj we get // But what if a = 0? 1 - // One particular “particular solution" has A = 0. Example 8.2.1: The Towers of Hanoi The recurrence equation for the number of moves in the Towers of Hanoi problem is a first-order linear recurrence equation: Tn = 2Tn-1+1. C 1 Here a =2 and c = 1, so 1 = -1, and any sequence T that satisfies — а 1 this RE is given by the formula Tn = 2" [1 – (-1)] +(-1) = 2" [I+ 1] – 1.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

Solve the ff missing with complete solutions
Solve this recurrence equation T(1) = 1 T(n) = T(n/2) + bnlogn
Use induction to verify the candidate solution to the following recurrence equation: tn = tn−1 + 5 for n > 1t1 = 2 The candidate solution is tn = 5n − 3.
What are the solutions of the linear congruence 3x == 4 (mod 7)?
Find all solutions of the following congruence(s). Show all work. 2x ≡ 5 mod 7 2x ≡ 5 mod 89
Solve each of the following congruences. (Give the complete list of solutions) (a) 2x^3 + 3x^2 + x + 1 ≡ 0 ( mod 5)
Solving the following Recurrences Using Induction Consider the recurrence tn=2tn-1 +1, n≥1 with initial condition t0=0. Obtain the solution using the substitution method.
Solve the following and show all worki) 34 % 5ii) 14 + 5 % 2 - 3iii) 4 % 6
give example of a function and prove that the function is both in big-omega of n^2 and small omega of n^2
. Write down the C++ code for Jacobi method to solve the following linear systems with .
Find all solutions to the congruence5x−3 = 4 (mod 25). If none exists, explain why. If there are one or more solutions, give a complete list of solution(s)
Use the Master Theorem to solve the recurrence equation. DETAILED steps and proofs are required. T(n)=15T(n/7)+n2lgn