Use the Principle of Mathematical Induction to show that the given statement is true for all natural

Question:

Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.

1 + 5 + 5² + … + 5^n-1 = 1/4(5n – 1)

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

Step by Step Answer:

Related Book For book-img-for-question

Precalculus

ISBN: 978-0321716835

9th edition

Authors: Michael Sullivan

See More Books

Question Posted: Apr 04, 2019 01:12 PM

See More Questions

Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 1 3 + 2 3 + 3 3 + + n 3 = n 2 (n + 1) 2
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 4 + 3 + 2 + ... + (5 - n) = 1/2n(9 - n)
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. -2 - 3 - 4 - ... - (n + 1) = - 1/2n(n + 3)
In Exercises 116, evaluate each algebraic expression for the given value or values of the variable(s). x 2 - 4(x - y), for x = 8 and y = 3
"To an economist, a resource is 'scarce' only if it has a positive price. Resources with zero prices are, by definition, not scarce." Do you agree? Or does the term scarce convey some other meaning?
Simplify each of the following and collect the like terms. (5s - 2t) - (2s - 4t)
Consider a person with constant relative risk aversion . (a) Verify that the fraction of wealth she will pay to avoid a gamble that is proportional to wealth is independent of initial wealth (that...
1. How important were the NYCAPS and CityTime projects for New York City? What were their objectives? What would have been their business benefits? 2. Evaluate the key risk factors in both projects....
Required information [The following information applies to the questions displayed below.] Forten Company's current year income statement, comparative balance sheets, and additional information...
Four OH variances; journal entries Kemp Manufacturing set 210,000 direct labor hours as the annual capacity measure for computing its predetermined variable overhead rate. At that level, budgeted...
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 1 + 4 + 4 2 + + 4n-1 = 1/3(4 n 1)
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. ( + 1) +1 1.2 2.3 3.4
The Medina and Haley Dental Clinic provides both preventive and orthodontic dental services. The two owners, Martin Medina and Cybil Haley, operate the clinic as two separate investment centres:...
int rFibNum(int a, int b, int n) { if(n == 1) return a; else if( n == 2) return b; else return rFibNum(a,b, n-1) + rFibNum(a, b, n-2); } In the code above; a) how many base cases are there? b) what...
Watch the Super Nanny (i.e., Jo Frost) episode "The Orm Family" (Season 1, Episode 3) and answer the following questions. Unless otherwise specified, your answers should focus on Declan (the 3 year...
2. Suppose Ford officials were asked to justify their decision. What moral principles do you think they would invoke? Assess Ford's handling of the Pinto from the perspective of each of the moral...
2. You have been asked to design the proto-type of an Automatic Grocery Vending Machine 10 (AGVM) for the super store. Automatic Grocery Vending Machine (AGVM) is a machine where different types of...
1. What does Porter's 5 Forces analysis strategy do? 2. Do most people agree Why? or disagree with this aspect Why? Here is the reference video, https://www.youtube.com/watch?v=Dfp23xSqpdk 3. What...
St. Marie Company is authorized to issue 1,000,000 shares of $5 par value preferred stock, and 5,000,000 shares of $1 stated value common stock. During the year, the company has the following...
Given that all the choices are true, which one concludes the paragraph with a precise and detailed description that relates to the main topic of the essay? A. NO CHANGE B. Decades, X-ray C. Decades...
Problems 3443. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus....
In Problems 1956, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 1930, graph the lines of the system. x + y 2x 9 2 = 13 7 = 3y + 2z =
In Problems 1750, find the partial fraction decomposition of each rational expression. x2 x3 4x2 + 5x - 2
A company has net income of $196,000, a profit margin of 9.7 percent, and an accounts receivable balance of $135,370. Assuming 70 percent of sales are on credit, what is the companys days sales in...
Hrubec Products, Incorporated, operates a Pulp Division that manufactures wood pulp for use in the production of various paper goods. Revenue and costs associated with a ton of pulp follow: Selling...
The AICPA guidelines suggest that taxes should be transparent and visible. This means that: a. The taxes affect similarly situated taxpayers in a similar manner. b. Taxes should be due at the same...

Use the Principle of Mathematical Induction to show that the given statement is true for all natural

Question:

Step by Step Answer:

I n1 51 and 511 1 II If 155 5k 5...View the full answer

Precalculus

Students also viewed these Mathematics questions