1. The following picture shows a 5 × 5 square that has been subdivided in a particular way. A. Write down an infinite series that gives the total area of the orange squares. (You should imagine the orange squares extending to the corners of the large 5 x 5 square ad infinitum e .) B. Calculate the sum of the infinite series you wrote down in part A. Then explain how the value of this sum can be inferred just from looking at the picture. 2. After receiving a $1400 stimulus check, you cash the check and stuff the cash into a mattress. You then form a plan: Over the course of every year, you will stuff an additional $200 into the mattress, and at the end of each year, you will remove 10% of the money in the mattress and use it to buy yourself something nice. As the years go by, the amount of money in your mattress will approach some fixed value. What is this value?
1. The following picture shows a 5 × 5 square that has been subdivided in a particular way. A. Write down an infinite series that gives the total area of the orange squares. (You should imagine the orange squares extending to the corners of the large 5 x 5 square ad infinitum e .) B. Calculate the sum of the infinite series you wrote down in part A. Then explain how the value of this sum can be inferred just from looking at the picture. 2. After receiving a $1400 stimulus check, you cash the check and stuff the cash into a mattress. You then form a plan: Over the course of every year, you will stuff an additional $200 into the mattress, and at the end of each year, you will remove 10% of the money in the mattress and use it to buy yourself something nice. As the years go by, the amount of money in your mattress will approach some fixed value. What is this value?
Chapter9: Sequences, Probability And Counting Theory
Section: Chapter Questions
Problem 23RE: Use the formula for the sum of the first ii terms of an arithmetic series to find the sum of the...
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Transcribed Image Text:1. The following picture shows a 5 x 5 square that has been subdivided in a particular way.
A. Write down an infinite series that gives the total area of the orange squares. (You should imagine the orange squares extending to the corners of the large 5 x 5 square ad infinitum e.)
B. Calculate the sum of the infinite series you wrote down in part A. Then explain how the value of this sum can be inferred just from looking at the picture.
2. After receiving a $1400 stimulus check, you cash the check and stuff the cash into a mattress. You then form a plan: Over the course of every year, you will stuff an additional $200 into the mattress, and at the end of
each year, you will remove 10% of the money in the mattress and use it to buy yourself something nice. As the years go by, the amount of money in your mattress will approach some fixed value. What is this value?
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