DISCRETE MATH8th EditionROSEN Publisher: MCG CUSTOMISBN: 9781266712326
DISCRETE MATH
Solutions for DISCRETE MATH
Problem 3E:
What are the terms a0,a1,a2 , and a3 of the sequence {an} , where an equals 2n+2? (n+1)n+1? n/2?...Problem 4E:
What are the terms a0,a1,a2 , and a3 of the sequence {an} , where an equals (2)n? 3? 7+4n? 2n+(2)n?Problem 5E:
List the first 10 terms of each of these sequences. the sequence that begins with 2 and in which...Problem 6E:
List the first lo terms of each of these sequences. the sequence obtained by starting with 10 and...Problem 7E:
Find at least three different sequences beginning with the terms 1, 2, 4 whose terms are generated...Problem 8E:
Find at least three different sequences beginning with the terms 3, 5, 7 whose terms are generated...Problem 9E:
Find the first five terms of the sequence defined by each of these recurrence relations and initial...Problem 10E:
Find the first six terms of the sequence defined by each of these recurrence relations and initial...Problem 11E:
Let an=2n+53n for n=0,1,2,,... Find a0,a1,a2,a3 , and a4 . Show that a2=5a16a0 , a3=5a26a1 , and...Problem 12E:
Show that the sequence {an} is a solution of the recurrence relation an=3an1+4an2 if an=0 . an=1 ....Problem 13E:
Is the sequence {an} a solution of the recurrence relation an=8an116an2 if an=0? an=1? an=2n? an=4n?...Problem 14E:
For each of these sequences find a recurrence relation satisfied by this sequence. (The answers are...Problem 15E:
Show that the sequence {an} is a solution of the recurrence relation an=an1+2an2+2n9 if an=n+2 ....Problem 16E:
Find the solution to each of these recurrence relations with the given initial conditions. Use an...Problem 17E:
Find the solution to each of these recurrence relations and initial conditions. Use an iterative...Problem 18E:
A person deposits $1000 in an account that yields 9% interest compounded annually. Set up a...Problem 19E:
Suppose that the number of bacteria in a colony triples every hour. Set up a recurrence relation for...Problem 20E:
Assume that the population of the world in 2017 was 7.6 billion and is growing at the rate of 1.12%...Problem 21E:
A factory makes custom sports cars at an increasing rate. In the first month only one car is made,...Problem 22E:
An employee joined a company in 2017 with a starting salary of $50,000. Every year this employee...Problem 23E:
Find a recurrence relation for the balance B(k) owed at the end of k months on a loan of $5000 at a...Problem 24E:
Find a recurrence relation for the balance B(k) owed at the end of k months on a loan at a rate of r...Problem 25E:
For each of these lists of integers, provide a simple formula or rule that generates the terms of an...Problem 26E:
For each of these lists of integers, provide a simple formula or rule that generates the terms of an...Problem 27E:
*27. Show that if an denotes the nth positive integer that is not a perfect square, then an=n+{n} ,...Problem 28E:
Let an , be the nth term of the sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6,...Problem 31E:
What is the value of each of these sums of terms of a geometric progression? j=0832j j=182j j=28(...Problem 32E:
Find the value of each of these sums. j=08(1+ ( 1 )j) j=18(3j2j) j=08(23j+32j) j=08(2 j+12j)Problem 33E:
Compute each of these double sums. i=12j=13( i+j) i=02j=03( 2i+3j) i=13j=02i i=02j=13ijProblem 34E:
Compute each of these double sums. i=13j=12( i+j) i=03j=02( 3i+2j) i=13j=02j i=02j=03i2j2Problem 35E:
Show that j=1n(aja j1)=ana0 , where a0,a1,...,an is a sequence of real numbers. This type of sum is...Problem 37E:
Sum both sides of the identity k2(k21)2=2k1 from k=1 to k=n and use Exercise 35 to find a formula...Problem 38E:
Use the technique given in Exercise 35, together with the result of Exercise 37b, to derive the...Problem 39E:
Find k=100200k . (Use Table 2.) TABLE 2 Some Useful Summation Formulae. Sum Closed Form k=0nark(...Problem 41E:
Find k=1020k2(k3) . (Use Table 2.) TABLE 2 Some Useful Summation Formulae. Sum Closed Form k=0nark(...Problem 42E:
Find . k=1020(k1)(2k2+1) (Use Table 2.) TABLE 2 Some Useful Summation Formulae. Sum Closed Form...Problem 45E:
There is also a special notation for products. The product of am,am+1,...,an is represented by...Problem 46E:
Express n! using product notation.Problem 47E:
Find j=04j! .Problem 48E:
Find j=04j! .Browse All Chapters of This Textbook
Chapter 1 - The Foundations: Logic And ProofsChapter 1.1 - Propositional LogicChapter 1.2 - Applications Of Propositional LogicChapter 1.3 - Propositional EquivalencesChapter 1.4 - Predicates And QuantifiersChapter 1.5 - Nested QuantifiersChapter 1.6 - Rules Of InferenceChapter 1.7 - Indroduction To ProofsChapter 1.8 - Proof Methods And StrategyChapter 2 - Basic Structures: Sets, Functions, Sequences, Sums, And Matrices
Chapter 2.1 - SetsChapter 2.2 - Set OperationsChapter 2.3 - FunctionsChapter 2.4 - Sequences And SummationsChapter 2.5 - Cardinality Of SetsChapter 2.6 - MatricesChapter 3 - AlgorithmsChapter 3.1 - AlgorithmsChapter 3.2 - The Growth Of FunctionsChapter 3.3 - Complexity Of AlgorithmsChapter 4 - Number Theory And CryptographyChapter 4.1 - Divisibility And Modular ArithmeticChapter 4.2 - Integer Representations And AlgorithmsChapter 4.3 - Primes And Greatest Commom DivisiorsChapter 4.4 - Solving CongruencesChapter 4.5 - Applications Of CongruencesChapter 4.6 - CryptographyChapter 5 - Induction And RecursionChapter 5.1 - Mathematical InductionChapter 5.2 - Strong Induction And Well-orderingChapter 5.3 - Recursive Definitions And Structural InductionChapter 5.4 - Recursive AlgorithmsChapter 5.5 - Program CorrectnessChapter 6 - CountingChapter 6.1 - The Basics Of CountingChapter 6.2 - The Pigeonhole PrincipleChapter 6.3 - Permutations And CombinationsChapter 6.4 - Binomial Coefficients And IdentitiesChapter 6.5 - Generalized Permutations And CombinationsChapter 6.6 - Generating Permutations And CombinationsChapter 7 - Discrete ProbabilityChapter 7.1 - An Introduction To Discrete ProbabilityChapter 7.2 - Probability TheoryChapter 7.3 - Bayes' TheoremChapter 7.4 - Expected Value And VarianceChapter 8 - Advanced Counting TechniquesChapter 8.1 - Applications Of Recurrence RelationsChapter 8.2 - Solving Linear Recurrence RelationsChapter 8.3 - Divide-and-conquer Algorithms And Recurrence RelationsChapter 8.4 - Generating FunctionsChapter 8.5 - Inclusion-exclusionChapter 8.6 - Applications Of Inclusion-exclusionChapter 9 - RelationsChapter 9.1 - Relations And Their PropertiesChapter 9.2 - N-ary Relations And Their ApplicationsChapter 9.3 - Representing RelationsChapter 9.4 - Closures Of RelationsChapter 9.5 - Equivalence RelationsChapter 9.6 - Partial OrderingsChapter 10 - GraphsChapter 10.1 - Graphs And Graph ModelsChapter 10.2 - Graph Terminology And Special Types Of GraphsChapter 10.3 - Representing Graphs And Graph IsomorphismChapter 10.4 - ConnectivityChapter 10.5 - Euler And Hamilton PathsChapter 10.6 - Shortest-path ProblemsChapter 10.7 - Planar GraphsChapter 10.8 - Graph ColoringChapter 11 - TreesChapter 11.1 - Introduction To TreesChapter 11.2 - Applications Of TreesChapter 11.3 - Tree TraversalChapter 11.4 - Spanning TreesChapter 11.5 - Minimum Spanning TreesChapter 12 - Boolean AlgebraChapter 12.1 - Boolean FunctionsChapter 12.2 - Representing Boolean FunctionsChapter 12.3 - Logic GatesChapter 12.4 - Minimization Of CircuitsChapter 13 - Modeling ComputationChapter 13.1 - Languages And GrammarsChapter 13.2 - Finite-state Machines With OutputChapter 13.3 - Finite-state Machines With No OutputChapter 13.4 - Language RecognitionChapter 13.5 - Turing MachinesChapter A - Appendices
Sample Solutions for this Textbook
We offer sample solutions for DISCRETE MATH homework problems. See examples below:
Chapter 1, Problem 1RQA set P is a subset of Q if each element of P is also the element of Q. We have to show that P is a...Chapter 3, Problem 1RQChapter 4, Problem 1RQChapter 5, Problem 1RQChapter 6, Problem 1RQChapter 7, Problem 1RQChapter 8, Problem 1RQIn mathematics, a binary relation on a set A is a set of ordered pairs of elements of A defined as...
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