Question: Let n > 1 be a positive integer. Prove combinatorially that n = n(n+ 1)2-2. k k=1 [Hint 1: Suppose that out of n

Let n > 1 be a positive integer. Prove combinatorially that n

Let n > 1 be a positive integer. Prove combinatorially that n = n(n+ 1)2"-2. k k=1 [Hint 1: Suppose that out of n people, anyone is permitted to register for a race. Everyone who registers may run twice. Gold and Silver medals are to be awarded, and the same person can win both medals. Everyone else gets a participation trophy.] [Hint 2: n(n + 1) = n(n 1) + 2n]

Step by Step Solution

★★★★★

3.43 Rating (159 Votes )

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

Document Format (2 attachments)

63633a7a729f4_237160.pdf

180 KBs PDF File

63633a7a729f4_237160.docx

120 KBs Word File

Students Have Also Explored These Related Mathematics Questions!

Let x(n), 0 n N 1 be a finite-duration sequence, which is also real-valued and even. Show that the zeros of the polynomial X(z) occur in mirror-image pairs about the unit circle. That is, if z =...

Let a be a positive integer and p be a prime. Consider the set of circular necklaces with p equally spaced beads, each of which is colored in one of a colors. (a) How many necklaces are there in...

Prove that 2n > n2 if n is an integer greater than 4.

San Terra Computers competed exclusively in the computer industry and generated approximately 98 % of its revenue from the sales of computers and computer - related software and approximately 2 % of...

This question involves the use of AGGREGATE linear PYTHOIN regression on the Auto data set. (a) Perform a simple linear regression with mpg as the response and horsepower as the predictor. Describe...

\f 134 THE BIG SQUEEZE munications Workers of America that has sought to unionize high"tech workers. "They hire whomever Microsoft tells them to put on their payroll. Then they p~ocess their...

Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...

Read the Peppercorn Dining Case on pages 228-256 in your text. As you read, think like an OD practitioner. We will break the Peppercorn Dining Case Study into 2 assignments. This assignment will...

Chapter One: Valuing Diversity R The wise are as rare as eagles that fly high in the sky. Bantu proverb Managing Workplace Diversity I Chapter One: Valuing Diversity VALUING DIVERSITY Chapter...

Elton Weiss and Reyna Herrera-Weiss are married and report the following income items: Eltons salary is $ 254,000 Reynas Schedule C net profit 50,000 The income tax deduction for Reyna's SE tax was...

1)Jack works for a polymer firm that has developed a new insulation material that has the potential to make newly constructed homes more energy efficient. He is asked to develop a voice of the...

BPR always involves automation. Group of answer choices True False

P.14 A clinic specializes in shoulder injuries. A patient is randomly selected from the population of all clinic clients. Let S be the number of doctor visits for shoulder problems in the past six...

You have decided to take your experience working with Jones Surf Shop and Pacific Surfboard and start a consulting firm of your own. Your first client is Playtime, inc. Playtime's primary business is...

Delcom ltd is planning to introduce a new product. Market research information suggest that the product should sell 100,000 units over its lifecycle at a price of Ksh 420 per unit. The company seeks...

You have just been hired as a new management trainee by Earrings Unlimited, a distributor of earrings to various retail outlets located in shopping malls across the country. In the past, the company...

Briefly discuss the implications of the financial statement presentation project for the reporting of stockholders equity.

Determine whether each of the following statements is true or false. If the statement is false, provide a counterexample. (a) [a] = [a] for all a Z. (b) [a] = [a] for all R. (c) [a] = [a] - 1 for...

Given the sequences a0, a1, a2, . . . and b0, b1,b2, ..., with exponential generating functions f(x), g(x), respectively, show that if h{x) = f(x)g(x), then h{x) is the exponential generating...

If G = (V, E) is a loop-free undirected graph, prove that G is a tree if there is a unique path between any two vertices of G.

A random variable is known to be normally distributed with the following parameters: = 5.5 and = 0.50 a. Determine the value of x such that the probability of a value from this distribution...

The Anasazi Real Estate Company has 20 listings for homes in Santa Fe, New Mexico. The number of days each house has been on the market without selling is as follows: a. Considering these 20 values...

Team Marketing Report (TMR) produces the Fan Cost Index (FCI) survey, now in its 16th year, which tracks the cost of attendance for a family of four at National Football League (NFL) games. The FCI...