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Sequence on a calculator Let {xn} be generated by the

Chapter 1, Problem 56RE

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QUESTION:

Pages of circles On page 1 of a book, there is one circle of radius . On page 2, there are two circles of radius . On page  there are  circles of radius .

a. What is the sum of the areas of the circles on page  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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QUESTION:

Pages of circles On page 1 of a book, there is one circle of radius . On page 2, there are two circles of radius . On page  there are  circles of radius .

a. What is the sum of the areas of the circles on page  of the book?

b. Assuming the book continues indefinitely (n → ∞), what is the sum of the areas of all the circles in the book?

ANSWER:

Step 1 of 3

a)

There are  circles on th page ,each of which has a radius

So,the sum of the reas equals to number of circles  

Sum of the ares

 

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