Question: For n, k Z+, prove that [n/k] = [n - 1)/k] + 1.

For n, k ∈ Z+, prove that [n/k] = [n - 1)/k] + 1.

Step by Step Solution

★★★★★

3.40 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Proof Case 1 fcjn Here n qk for q Z and n 1 k qk 1 k q 1 k wi... View full answer

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 (1 attachment)

Word file Icon

954-M-L-A-L-S (7638).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

For f, g: Z+ R, we say that f is "big Theta of g," and write f (g), when there exist constants m1, m2 R+ and k Z+ such that m1|g(n)| Prove that f ...

Q:

For any real sequence define a) Prove that if lim infkxk > x for some x R, then xk > x for k large. b) Prove that if xk x as k , for some x R, then lim infk xk = x. c) If ak > 0 for all k N, prove...

Q:

Let vt,... , v" be elements of a complex inner product space. Let K denote the corresponding n x n Gram matrix, defined in the usual manner. (a) Prove that A- is a Hermitian matrix, as defined in...

Q:

Exercise 3.17. Let Y Uniform([0, 1]) and X Binomial(n,Y ). (i) Use iterated expectation for probability to write P(X = k) = n k !Z 1 0 y k (1 y) nk d y. (1) (ii) Write An,k = R 1 0 y k (1 y) nk d y....

Q:

82. Let X1,X2, . . . be independent continuous random variables with a common distribution function F and density f = F, and for k 1 let Nk = min{n k: Xn = kth largest of X1, . . . ,Xn} Hint: Use...

Q:

1. What is the correct formula for C(n, k) = "n choose k" = the number of ways of choosing k elements out of a set of cardinality n? O C(n, k) = n!/k! O cn, k) = n!/(n - k)! O C(n, k) = n!/(k! * (n -...

Q:

Let X1,X2, . . . be independent continuous random variables with a common distribution function F and density f = F , and for k 1 let Hint: Use induction. First prove it when k = 2, and then assume...

Q:

1) a) Define the sets A = {2n + 1 | n Z}, B = {3m + 2 | m Z}, C = {12k + 5 | k Z}. Prove that C A B. Hint: Prove that C A B, and then find an element of A B that is not in C to show that the sets are...

Q:

Let n Z+ with n > 1. a) If n = 2k where k is an odd integer, prove that k3 =k (mod n). b) If n = 4k for some k Z+, prove that (2k)2 = 0 (mod ft). c) Prove that 10(modn), otherwise. with or n even...

Q:

Chapter 15, \"More Probability\" from Applied Finite Mathematics by Rupinder Sekhon was developed by OpenStax College, licensed by Rice University, and is available on the Connexions website. It is...

Q:

The little-league coach recruits 9 players in total. In how many ways can the coach select 9 players from the 9-player roster? The order in which 9 players are selected is important. 362,880 312,450...

Q:

What is a confidence-interval estimate of a parameter? Why is such an estimate superior to a point estimate?

Q:

What are the advantages of effective personal financial planning?

Q:

Think about the various flavors of chocolate blocks: dark, mint, ginger, and chilli. Suppose the price of all mint chocolate blocks increases. Would this affect the sales of that type of chocolate?...

Q:

Multiply. Assume that all exponents are integers. (a) (ta + t-a)2 (b) (an - bn)3

Q:

Consider the numbers 6 6/7, 12, 0, -13/4, 38, - 1.2, 29, -5 (a) Which are whole numbers? (b) Which are irrational numbers? (c) Which are integers but not natural numbers? (d) Which are rational...

Q:

Compute and write scientific notation for the answer: 2.7 104 / 3.6 10-3

Q:

Cash fow to the waman under an interest-only loan, in which Poryi will pay the annual intecest expense each year and pay the principal back at the end of the contract What is the amount of payment...

Q:

A project will produce operating cash flows of $45,000 a year for four years. During the life of the project, inventory will be lowered by $30,000 and accounts receivable will increase by $15,000....

Q:

30. Consider the market for one-year discount bonds with standard face value of $1,000. Assume that supply and demand curves in this market are both linear, and Q$ = P 700, while demand curve passes...