(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,
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Part b
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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