Use induction to prove that (n^{3}-n) is divisible by 3 for all natural numbers (n).

Question:

Use induction to prove that $n^{3}-n$ is divisible by 3 for all natural numbers $n$.

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

Step by Step Answer:

Related Book For answer-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Jan 28, 2024 12:02 AM

See More Questions

In this question we study the recursively defined functions f, g and h given by the following defining equations f(0) = 1 base case 0, f(1) = 0 base case 1, and f(n) = n f(n 1) + f(n 2)^2...
2. Water leaves a faucet with a downward velocity of 5.2 m/s. As the water falls below the faucet, it accelerates with acceleration g. The cross sectional area of the water stream leaving the faucet...
Another phrase for "Common Law" is: National Law International Law Case Law Natural Law Civil Law
You are the manager of a fast food restaurant. Part of your job is to report to the boss at the end of the day which special is selling best. Use your vast knowledge of descriptive statistics and...
Pilots can be tested for the stresses of flying high-speed jets in a whirling human centrifuge which takes 1.0min to turn through 20 complete revolutions before reaching its final speed. (a) What was...
Daisey Company is a very profitable small business. It has not, however, given much consideration to internal control. For example, in an attempt to keep clerical and office expenses to a minimum,...
In 2004, Jui-Chen Lin, a citizen of China, entered into an agreement with Robert Chiu and Charles Cobb, citizens of the United States, to form an LLC to acquire and operate a fast-food restaurant in...
The Solo Hotel opened for business on May 1, 2014. Here is its trial balance before adjustment on May 31 Other data: 1. Insurance expires at the rate of $450 per month. 2. A count of supplies shows...
v = [-21 0]T V = [101]T V1 Are the basis vectors v and v orthogonal? (Provide proof of your answer) the current basis vectors are not orthogonal, use projection to find v, the component of v...
Use induction to prove that $5^{2 n}-4^{n}$ is divisible by 7 for all natural numbers $n$.
Use induction to prove that $f(n)=8^{n}-1$ is divisible by 7 for all natural numbers $n$. For the induction step, show that \[ 8^{k+1}-1=7 \cdot 8^{k}+\left(8^{k}-1ight) \]
The United States Constitution is among the finest legal accomplishments in the history of the world. Which of the following influenced Ben Franklin, Thomas Jefferson, and the rest of the Founding...
GreenEnergy Inc., a renewable energy firm being evaluated for a private equity investment, acquired a new wind turbine system in late 2024 for a total cost of $50 million. Considering the relevant...
City Art Museum (CAM) purchased the copyright to a piece of artwork for $962,000 CAM PLANTS TO REPRODUCE 1.8 millon posters of the artwork over a period of 10 years. Assuming CAM uses the...
A company purchases supplies on account for $2,300. Indicate the amount of increases and decreases in the accounting equation. Assets Liabilities + Stockholders' Equity +
A 1 . 0 C charge experiences a 1 0 N downward force in an electric field. What force would a 1 . 0 C charge experience in the same field?
FNSFMB512 - CP2 - RP - Call Conversation (Allan Parker) v1.0 According to your analysis and findings from the previous activities, you are to call Allan to: Discuss his special financial needs...
Which amortization method is required for intangibles? Are there any exceptions?
Consider a game of poker being played with a standard 52-card deck (four suits, each of which has 13 different denominations of cards). At a certain point in the game, six cards have been exposed. Of...
Determine whether the series converges or diverges. 1/ %31
Determine whether the series converges or diverges. ! 31
Determine whether the series converges or diverges.
The stockholders' equity accounts of the subsidiary are eliminated Multiple select question. against the Investment account. to avoid double-counting net assets of the subsidiary. permanently on the...
Select all that apply Minority-passive equity investments generally Multiple select question. have changes in fair value accounted for in net income. are accounted for at fair value. are accounted...
During the year ended 3 0 June 2 0 1 4 , Parent company guarantees borrowings of Subsidiary company which amounts to $ 1 , 0 0 0 , 0 0 0 . At the time of the guarantee, Subsidiary s financial...

Use induction to prove that (n^{3}-n) is divisible by 3 for all natural numbers (n).

Question:

Step by Step Answer:

Calculus

Students also viewed these Mathematics questions