Show that the sum of the first 2n natural numbers is n(2n + 1).

Question:

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

Step by Step Answer:

Related Book For book-img-for-question

Pearson Edexcel A Level Mathematics Pure Mathematics Year 2

ISBN: 9781292183404

1st Edition

Authors: Greg Attwood, Jack Barraclough, Ian Bettison, David Goldberg, Alistair Macpherson, Joe Petran

See More Books

Question Posted: Aug 07, 2023 02:50 AM

See More Questions

The process of adding rational functions (ratios of polynomials) by placing them over a common denominator is the analogue of adding rational numbers. The reverse process of taking a rational...
(a) Show that, for any positive integer n, 1 + 2 + 4 + 8 +g+ 2n = 2n+1 - 1. (b) Show that the sum of the elements of any row of Pascal's triangle equals one more than the sum of the elements of all...
(a) Show that the number of electron states in a sub-shell is 4 + 2. (b) By summing the number of states in each of subshells, show that the number of states in a shell is 2n 2 . Use the fact that...
For each of these utility functions, find the optimal consumption choices z and y for a consumer with budget w = 1, who faces prices pz = 0.05 and Py = 0.3. Are the goods substitutes or complements,...
On January 1, 2010, the Fastor Company had a retained earnings balance of $218,600. It is subject to a 30% corporate income tax rate. During 2010, the company earned net income of $67,000, and the...
If Ann and Zack form a cartel and produce the same quantity of rides as would be produced in monopoly, what are the quantity of rides, the price of a ride, and the economic profit of Ann and Zack?...
Under the debt financing alternative, only $100,000 is required at CF0 and the project will provide an annual return after debt service of $18,000 for each of the 5 years. In addition, the reversion...
Discussion Problem: The Margo Manufacturing Company is performing an annual evaluation of one of its suppliers, the Mimi Company. Bo, purchasing manager of the Margo Manufacturing Company, has...
Hudson Corporation will pay a dividend of $5.80 per share next year. The company pledges to increase its dividend by 4.20 percent per year indefinitely. If you require a return of 13.40 percent on...
Given that the geometric series 1 2x + 4x 2 8x 3 + is convergent, a. Find the range of possible values of x. b. Find an expression for S in terms of x.
Prove that the sum of the first 50 natural numbers is 1275.
A difference between the innate immune system and the acquired immune system is (a) the innate immune system includes many more different types of receptors than the acquired immune system. (b) the...
You have recently taken over daycare center that was under substandard leadership. Currently, the staff is unmotivated, negative, and often absent from work. You notice that there is minimal...
Choose an organization from the industry of your choice to discuss, illustrate, and reflect deliberately on the following: Why is it important to distinguish between "group" and "team "? What kinds...
The focus of data governance programs, in some capacity, is enterprise-wide data quality standards and processes. If you were a manager focusing on master data: Would you likely meet enterprise-level...
1) Identify and explain each component of the ANOVA model. 2) How is the F ratio obtained? 3) What role does the F ratio play?
Make a BCG matrix table and place the following products from Apple: iPhone, iPad, iMac, iPod, Apple TV, Apple Watch, AirPod, and HomePod. Briefly describe why you have placed the products in the...
Why would it be economically efficient to require a natural monopoly to charge a price equal to marginal cost? Why do most regulatory agencies require natural monopolies to charge a price equal to...
Representative data read from a plot that appeared in the paper Effect of Cattle Treading on Erosion from Hill Pasture: Modeling Concepts and Analysis of Rainfall Simulator Data (Australian Journal...
A researcher is interested in whether listening to classical music improves spatial ability. She randomly assigns subjects to either a classical music condition or a no-music condition. Is this a...
How does using a Latin square aid a researcher in counterbalancing a study?
What are the similarities and differences between within-subjects and matched-subjects designs?
Provide a graph chart or data with sample numbers indicating Valuing Stocks and Bonds?
I just need help with part b. It says that the answer is not complete and some are wrong. So can you kindly fix it for me and give me the full answers as it says the answer is "not complete". Thank...
What is Coke's average ownership percentage in its equity method investments? Goodwill is 7000 Calculate the firm's current ratio (current assets/current liabilities). Calculate the current ratio...

Show that the sum of the first 2n natural numbers is n(2n + 1).

Question:

Step by Step Answer:

S2n 1 2 3 2n ...View the full answer

Pearson Edexcel A Level Mathematics Pure Mathematics Year 2

Students also viewed these Mathematics questions