Question: please answer 2 and 6 only Exercise 1.4 Prove the following statements. 1. Prove by induction on n> 1 that i1/2 = 1-1/2 2. Prove

please answer 2 and 6 only

Exercise 1.4 Prove the following statements. 1. Prove by induction on n> 1 that i1/2 = 1-1/2" 2. Prove by induction on n > 0 that _, 21 = 2n+1 - 1. 3. Prove ! (21 - 1) = np. 4. Prove that (n + 1)2 = O(na). 5. Prove 2 lg(n!) > n Ign, where n is a positive integer greater than 2. 6. The number generated by the formula na + n + 17 is prime for n > 0, where n is an integer. Either prove it or disprove it by counterexample

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Assigned Questions (1) Let an be the sequence defined recursively as follows: a1 = 1 a2 = 1 an = an - 1 + 1 for n > 3. 2 an - 2 Prove that an E [1, 2] for all n. (2) Recall that Di = n(n+ 1) i= 1 2...

Proof Creator 1 Problems MAT246 LEC0101, Fall 2021 Assignment Information Writing Tips: See the handout posted on the course website. Also the additional writing supports (writing centres, ELL...

ICS 3 1 1 : Algorithms Spring 2 0 2 4 Problem Set 1 Prof. Nodari Sitchinava Due: Friday, January 1 2 , 2 0 2 3 at 4 pm You may discuss the problems with your classmates, however you must write up the...

Please answer all questions on the white pieces of paper Financial statements Consolidated income statement Year ended 31 December 2009 All figures in f millions Notes 2009 2008 Continuing operations...

Discrete math (a) Prove by mathematical induction that: n^2 > n + 1 forall n greaterthanorequalto 2. (b) Use mathematical induction to prove the following statement. 1 + 2 + 2^2 + 2^3 + ... + 2^n =...

THIS IS THE QUESTION ABOUT THE D&L OF ALGORITHMS Design and Complexity Analysis QUESTION 1: give pseudocode for interpolation search, and analyze its worst-case complexity. Asymptotic Notation,...

there is no graph the question came like that Question 2: Recall that K, where n 2 is an integer, denotes the complete graph with n vertices. This graph has ) edges, i.e., one edge for each pair of...

1. Use the 3 step Mathematical Induction process to prove the following statements. You must label and show all three steps. Step 1: Prove n = 1 is true Step 2: Assume true for all n = k Step 3: plug...

Prove the following statements using induction. Each proof needs to be complete, including the basis step and induction step; each step in your proof needs to be justified (except when it follows by...

1) Use the Euclidean algorithm to find the GCD or 1326 and 2940. Please show each stage of the process. 2) Let f(1) = p2 and f(n+ 1) = p1 + f(n). Prove, by induction, that f(n) is irrational for all...

What level of confidence would accompany each of the following intervals? a. Sample proportion 1.0(SEP) b. Sample proportion 1.645(SEP) c. Sample proportion 1.96(SEP) d. Sample proportion ...

Write a paper in which discuss the following: 1. Evaluate the critical elements of accounting quality. Compare and contrast balance sheet quality with earnings quality. Explain why both are important...

Which financial metric provides insight into a company's profitability after all expenses, including taxes? Gross Profit Net Profit Before Tax ( NPBT ) Net Profit After Tax ( NPAT ) Earnings Before...

Takaful industry outlook remains positive despite Covid-19 KUALA LUMPUR: The Malaysian Takaful Association (MTA) remains positive of the performance of the local takaful industry this year despite...

Writing a Strong Introduction

Conclude with the same strength as in the introduction Prepare an effective outline?

Choose appropriate and powerful language Develop a strong introduction, a crucial part of all speeches