Prove that n 2 + n is divisible by 2 for any positive integer n.

Fantastic news! We've Found the answer you've been seeking!

Question:

Prove that n² + n is divisible by 2 for any positive integer n.

Related Book For answer-question

Linear Algebra with Applications

ISBN: 978-0131857858

7th edition

Authors: Steven J. Leon

See More Books

Posted Date: Apr 01, 2023 06:04 AM

See More Questions

Prove each of the following statements using mathematical induction. (a) Prove that for any positive integer n, s = - (n(n + ) ) 2 j=1 (b) Prove that for any positive integer n, j.2=(n-1)2+ +2 j=1...
(a) Prove by the Principle of Mathematical Induction that 9n 2" is divisible by 7 for any n EN+ (7 Marks) (b) Prove by contradiction: For any m e N+, if m? is divisible by 3 then m is divisible by 3...
Lior Silberman's Math 312: ComPAIR Assignment 2 This assignment is due Wednesday, 3/2/2021 at noon (Vancover time) Comparisons are due Sunday, 5/3/2021 at 11pm (Vancouver time). 1. Let n be a...
Read the Comp & Ben Case Study and answer the following question: To the degree job growth (and increased car sales that come from m costs) is based on two tier-wage structures, how sustainable...
Based on the following information, determine the net increase (decrease) in cash for Luther Corp. for the year ended December 31, 2012. Use the direct method to report cash flows from operating...
What is meant by baseline in a single-case design?
Evaluate the equilibrium constant at $600 \mathrm{~K}$ for the reaction \[ \mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g}) ightarrow \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g}) \] Data Table: 0...
The Pro Apparel Company manufactures baseball-style caps with various team logos. The caps come in an assortment of designs and colors. The company has had monthly sales for the past 24 months as...
5 Kayak Company budgeted the following cash receipts (excluding cash receipts from loans received) and cash payments (excluding cash payments for loan principal and interest payments) for the first...
Part of developing a long-term R&D strategy is to locate facilities in countries that are widely known to be competitive. Your company seeks to develop R&D facilities in Asia to counter recent...
Which device below handles a liquid and requires work input, usually with negligible heat transfer and negligible changes in kinetic and potential energies of fluid streams? (d) Pump (a) Nozzle (b)...
Suppose government spending increases. Would the effect on AD be larger if the central bank took no action in response, or if the central bank were committed to maintaining a fixed interest rate?...
Why is there concern over the loss of biodiversity?
How can the study of contemporary foragers provide us with an understanding of Paleolithic lifestyles?
Explain why feminist economists criticize the use of GDP as a measure of well-being.
What is the difference between sex and gender, and why is an understanding of this difference important in economic analysis?
Henry Inc. purchased $5,000 of Container Corporation's 5% bonds at par. The purchase is made on January 1, 2020, and the investment is classified as a commercial security. As of June 30, 2020, Henry...
Suppose that A is an m n matrix with linearly independent columns and the linear system LS(A, b) is consistent. Show that this system has a unique solution.
Construct a defective matrix by setting A = ones(6); A = A - tril(A) - triu(A, 2) It is easily seen that = 0 is the only eigenvalue of A and that its eigenspace is spanned by e1. Verify this by...
If a matrix is sensitive to roundoff errors, the computed value of its determinant may differ drastically from the exact value. For an example of this, set U = round(l00 * rand(l0)); U = triu((U, 1)...
Let S be the vector space of infinite sequences defined in Exercise 15 of Section 1. Let So be the set of {an} with the property an 0 as n . Show that So is a subspace of S.
A plane wall of a furnace is fabricated from plain carbon steel $\left(k=60 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, ho=7850 \mathrm{~kg} / \mathrm{m}^{3}, c=430 ight.$ \(\mathrm{J} / \mathrm{kg}...
A steel sphere (AISI 1010), $100 \mathrm{~mm}$ in diameter, is coated with a dielectric material layer of thickness $2 \mathrm{~mm}$ and thermal conductivity \(0.04 \mathrm{~W} / \mathrm{m} \cdot...
The heat transfer coefficient for hydrogen flowing over a sphere is to be determined by observing the temperature-time history of a sphere fabricated from pure copper. The sphere, which is \(20...

Prove that n 2 + n is divisible by 2 for any positive integer n.

Question:

Expert Answer:

The detailed answer for the above question is provided below n 2 n nn ... View the full answer

Linear Algebra with Applications

Students also viewed these mathematics questions