Explanation Explanation Given: The area of a new triangle at each stage is 1 8 of the area of a triangle at previous stage. That is, A 2 = 1 8 A 1 . The number of new triangle doubling at each stage. Result used: The geometric series ∑ n = 1 ∞ a r n − 1 = a + a r + a r 2 + ⋯ is convergent if | r | < 1 and its sum is a 1 − r , where a ≠ 0 is the first term and r is the common ratio of the series. Calculation: From the given, the second stage there are 2 triangles of area A 2 = 1 8 A 1 . In every stage, the new triangle doubles at each stage. At the n th stage, there are 2 n − 1 triangles of area A n = 1 8 A n − 1 . A n = 1 8 2 A n − 2 ⋮ A n = 1 8 n − 1 A 1 The total area of the triangles formed at the n th stage is 2 n − 1 8 n − 1 A 1 = ( 1 4 ) n − 1 A 1

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 8.3, Problem 77E

To determine

To show: The area of the region R is 43 times the area of A1.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.3, Problem 76E

Chapter 8.3, Problem 78E

Chapter 8 Solutions

Calculus: Early Transcendentals (2nd Edition)

Ch. 8.1 - Define sequence and give an example.Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Given the series k=1k, evaluate the first four...Ch. 8.1 - The terms of a sequence of partial sums are...Ch. 8.1 - Consider the infinite series k=11k. Evaluate the...Ch. 8.1 - Explicit formulas Write the first four terms of...Ch. 8.1 - Explicit formulas Write the first four terms of...

Additional Math Textbook Solutions

Find more solutions based on key concepts

The derivative of g(x)=x3(5.4)x.

Calculus and Its Applications (11th Edition)

Express the limits in Exercises 1–8 as definite integrals. 1. , where P is a partition of [0, 2]

University Calculus: Early Transcendentals (4th Edition)

In Example 1, what is the average velocity between t=2 and t=3? Example 1 Average Velocity A rock is launched v...

Calculus, Single Variable: Early Transcendentals (3rd Edition)

Suppose that the graph of a function f is known. Then the graph of y=f( x2 ) may be obtained by a(n) ______ shi...

Precalculus (10th Edition)

In Exercises 1–4, show that each function y = f(x) is a solution of the accompanying differential equation. 1. ...

Thomas' Calculus: Early Transcendentals (14th Edition)

Equation and complete the table of values

Glencoe Math Accelerated, Student Edition

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The area of the region R is 4 3 times the area of A 1 .

Solution Summary: The author calculates that the area of a new triangle at each stage is 18A_1.

Videos

To show: The area of the region R is 43 times the area of A1.

Want to see the full answer?

Chapter 8 Solutions

Additional Math Textbook Solutions