Pages of circles On page 1 of a book, there is one circle of radius 1.On page 2, there are two circles of radius 1/2. On page n, thereare 2n - 1 circles of radius 2-n + 1.a. What is the sum of the areas of the circles on page n of the book?b. Assuming the book continues indefinitely (n→ ∞), what is thesum of the areas of all the circles in the book?
Pages of circles On page 1 of a book, there is one circle of radius 1.On page 2, there are two circles of radius 1/2. On page n, thereare 2n - 1 circles of radius 2-n + 1.a. What is the sum of the areas of the circles on page n of the book?b. Assuming the book continues indefinitely (n→ ∞), what is thesum of the areas of all the circles in the book?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 46E
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Pages of circles On page 1 of a book, there is one circle of radius 1.
On page 2, there are two circles of radius 1/2. On page n, there
are 2n - 1 circles of radius 2-n + 1.
a. What is the sum of the areas of the circles on page n of the book?
b. Assuming the book continues indefinitely (n→ ∞), what is the
sum of the areas of all the circles in the book?
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