Introduction to Java Programming and Data Structures Comprehensive Version (11th Edition)
11th Edition
ISBN: 9780134700144
Author: Liang
Publisher: PEARSON
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Chapter 18, Problem 18.4PE
(Sum series) Write a recursive method to compute the following series:
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By dragging statements from the left column to the right column below, give a proof by induction of the following statement:
an
=
= 9" - 1 is a solution to the recurrence relation an = 9an-18 with ao
=
: 0.
The correct proof will use 8 of the statements below.
Statements to choose from:
Note that a₁ =
9a0 + 8.
Now assume that P(n) is true for all n ≥ 0.
Your Proof: Put chosen statements in order in this
column and press the Submit Answers button.
Let P(n) be the predicate, "a = 9″ – 1".
απ = 90 − 1 =
Note that
Let P(n) be the predicate, "an
9" - 1 is a
solution to the recurrence relation an = 9an-1 +8
with ao = 0."
-
Now assume that P(k + 1) is true.
Thus P(k) is true for all k.
Thus P(k+1) is true.
Then ak+1
=
9ak +8, so P(k + 1) is true.
= 1 − 1 = 0, as required.
Then = 9k — 1.
ak
Now assume that P(k) is true for an arbitrary
integer k ≥ 1.
By the recurrence relation, we have
ak+1 =
ak+1 =
= 9ak + 8 = 9(9k − 1) + 8
This simplifies to
9k+19+8 = 9k+1 − 1
Then 9k+1 − 1 = 9(9*…
Given the following request to an AI chatbot, which response is more accurate? (You should use Google to verify that the factual claims in each response are accurate.)
Prompt
Is this true? The first recorded use of the phrase "when pigs fly" in print is in a 1616 play by Ben Jonson called "The Devil is an Ass," in which a character says, "When pigs fly, good-night!!"
Response
Response A
Response B
Yes, that's true! The phrase "when pigs fly" indeed appears in Ben Jonson's 1616 play The Devil is an Ass and was said during the second act in a conversation between Fitzdottrel and Pug. The phrase was first used to express skepticism or disbelief, suggesting that something is as unlikely to happen as the fanciful idea of pigs flying. This usage is often cited as one of the earliest instances of the phrase in print.
The claim that the phrase "when pigs fly" was first recorded in Ben Jonson's 1616 play "The Devil is an Ass" is not accurate. There is no evidence from the…
This is for my Computer Organization & Assembly Language Class
Chapter 18 Solutions
Introduction to Java Programming and Data Structures Comprehensive Version (11th Edition)
Ch. 18.2 - What is a recursive method? What is an infinite...Ch. 18.2 - Prob. 18.2.2CPCh. 18.2 - Show the output of the following programs and...Ch. 18.2 - Prob. 18.2.4CPCh. 18.2 - Prob. 18.2.5CPCh. 18.2 - Write a recursive mathematical definition for...Ch. 18.3 - Prob. 18.3.1CPCh. 18.3 - What is wrong in the following methods?Ch. 18.3 - Prob. 18.3.3CPCh. 18.4 - Describe the characteristics of recursive methods.
Ch. 18.4 - Prob. 18.4.2CPCh. 18.4 - Prob. 18.4.3CPCh. 18.5 - Prob. 18.5.1CPCh. 18.5 - Prob. 18.5.2CPCh. 18.5 - What is a recursive helper method?Ch. 18.6 - Prob. 18.6.1CPCh. 18.6 - How does the program get all files and directories...Ch. 18.6 - How many times will the getSize method be invoked...Ch. 18.6 - Will the program work if the directory is empty...Ch. 18.6 - Will the program work if line 20 is replaced by...Ch. 18.6 - Will the program work if lines 20 and 21 are...Ch. 18.7 - Prob. 18.7.1CPCh. 18.8 - Prob. 18.8.1CPCh. 18.8 - Prob. 18.8.2CPCh. 18.8 - How many times is the displayTriangles method...Ch. 18.8 - Prob. 18.8.4CPCh. 18.8 - Prob. 18.8.5CPCh. 18.9 - Which of the following statements are true? a. Any...Ch. 18.9 - Prob. 18.9.2CPCh. 18.10 - Identify tail-recursive methods in this chapter.Ch. 18.10 - Rewrite the fib method in Listing 18.2 using tail...Ch. 18 - Prob. 18.1PECh. 18 - Prob. 18.2PECh. 18 - (Compute greatest common divisor using recursion)...Ch. 18 - (Sum series) Write a recursive method to compute...Ch. 18 - (Sum series) Write a recursive method to compute...Ch. 18 - (Sum series) Write a recursive method to compute...Ch. 18 - (Fibonacci series) Modify Listing 18.2,...Ch. 18 - Prob. 18.8PECh. 18 - (Print the characters in a string reversely) Write...Ch. 18 - (Occurrences of a specified character in a string)...Ch. 18 - Prob. 18.11PECh. 18 - (Print the characters in a string reversely)...Ch. 18 - (Find the largest number in an array) Write a...Ch. 18 - (Find the number of uppercase letters in a string)...Ch. 18 - Prob. 18.15PECh. 18 - (Find the number of uppercase letters in an array)...Ch. 18 - (Occurrences of a specified character in an array)...Ch. 18 - (Tower of Hanoi) Modify Listing 18.8,...Ch. 18 - Prob. 18.19PECh. 18 - (Display circles) Write a Java program that...Ch. 18 - (Decimal to binary) Write a recursive method that...Ch. 18 - (Decimal to hex) Write a recursive method that...Ch. 18 - (Binary to decimal) Write a recursive method that...Ch. 18 - (Hex to decimal) Write a recursive method that...Ch. 18 - Prob. 18.25PECh. 18 - (Create a maze) Write a program that will find a...Ch. 18 - (Koch snowflake fractal) The text presented the...Ch. 18 - (Nonrecursive directory size) Rewrite Listing...Ch. 18 - (Number of files in a directory) Write a program...Ch. 18 - (Game: Knights Tour) The Knights Tour is an...Ch. 18 - (Game: Knights Tour animation) Write a program for...Ch. 18 - (Game: Eight Queens) The Eight Queens problem is...Ch. 18 - Prob. 18.35PECh. 18 - (Sierpinski triangle) Write a program that lets...Ch. 18 - (Hilbert curve) The Hilbert curve, first described...Ch. 18 - (Recursive tree) Write a program to display a...Ch. 18 - Prob. 18.39PE
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