(22) We place line segments side by side on the real line starting at the origin and moving in the positive direction. Determine if there is a number N on the real line that will not be covered by the any of the segments. If such a number does not exist argue why. If numbers N exist then find among them the least one. Explain how you did this. a) I₁ = [0, 1), I₂ and subsequent intervals In have lengths equal to 50% of the length of their immediate left neighbors. b) I₁ = [0,1), I₂ has length equal to ½ of the length of the first one. The length of I3 is obtained from 1₂ by removing 25% of I2. In general the length of In+1 is obtained from In by removing of In+1.
(22) We place line segments side by side on the real line starting at the origin and moving in the positive direction. Determine if there is a number N on the real line that will not be covered by the any of the segments. If such a number does not exist argue why. If numbers N exist then find among them the least one. Explain how you did this. a) I₁ = [0, 1), I₂ and subsequent intervals In have lengths equal to 50% of the length of their immediate left neighbors. b) I₁ = [0,1), I₂ has length equal to ½ of the length of the first one. The length of I3 is obtained from 1₂ by removing 25% of I2. In general the length of In+1 is obtained from In by removing of In+1.
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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(22) We place line segments side by side on the real line starting at the origin and moving in
the positive direction. Determine if there is a number N on the real line that will not
be covered by the any of the segments. If such a number does not exist argue why. If
numbers N exist then find among them the least one. Explain how you did this.
a) I₁ = [0, 1), I₂ and subsequent intervals In have lengths equal to 50% of the length
of their immediate left neighbors.
b) I₁ = [0, 1), I₂ has length equal to of the length of the first one. The length of
I3 is obtained from I₂ by removing 25% of I2. In general the length of In+1 is obtained
from In by removing of In+1.
2n
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