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(b) Ugh is a Stone Age stone man. He is really good at making bricks. His intention is to make a bridge across a ravine by stacking bricks according to the picture below where the top brick has an overhang of 1/2, the second brick overhangs by 1/4, the third by 1/6, and so on with the n-th brick (on the bottom) having an overhang of 1/(2n). The total overhang is 1 1 1 1 1 + - + - + - +.. 4 2n 6. 8 Is there a maximum width ravine that can, in theory, be crossed in this manner? Explain,

(b) Ugh is a Stone Age stone man. He is really good at making bricks. His intention is to make a bridge across a ravine by stacking bricks according to the picture below where the top brick has an overhang of 1/2, the second brick overhangs by 1/4, the third by 1/6, and so on with the n-th brick (on the bottom) having an overhang of 1/(2n). The total overhang is 1 1 1 1 1 + - + - + - +.. 4 2n 6. 8 Is there a maximum width ravine that can, in theory, be crossed in this manner? Explain,

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...
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Part b 

1. (a) Use the integral test to show that the series 1 = 1 + 2 1 Σ 3 n>1 is divergent. As part of your answer, state the three conditions that a function f must satisfy before the integral test can be applied, and show that f(x) = 1/x does indeed satisfy these conditions. (b) Ugh is a Stone Age stone man. He is really good at making bricks. His intention is to make a bridge across a ravine by stacking bricks according to the picture below where the top brick has an overhang of 1/2, the second brick overhangs by 1/4, the third by 1/6, and so on with the n-th brick (on the bottom) having an overhang of 1/(2n). The total overhang is 1 + - + - + 4 1 +...+ 8 1 6. 2n Is there a maximum width ravine that can, in theory, be crossed in this manner? Explain.
Transcribed Image Text:1. (a) Use the integral test to show that the series 1 = 1 + 2 1 Σ 3 n>1 is divergent. As part of your answer, state the three conditions that a function f must satisfy before the integral test can be applied, and show that f(x) = 1/x does indeed satisfy these conditions. (b) Ugh is a Stone Age stone man. He is really good at making bricks. His intention is to make a bridge across a ravine by stacking bricks according to the picture below where the top brick has an overhang of 1/2, the second brick overhangs by 1/4, the third by 1/6, and so on with the n-th brick (on the bottom) having an overhang of 1/(2n). The total overhang is 1 + - + - + 4 1 +...+ 8 1 6. 2n Is there a maximum width ravine that can, in theory, be crossed in this manner? Explain.
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