8. Show that, at the n stage of the construction of the Cantor Middle- Thirds set, the sum of the lengths of the remaining intervals is Conclude that the sum of the lengths of these intervals tends to 0 as n → ∞o.

8. Show that, at the n stage of the construction of the Cantor Middle- Thirds set, the sum of the lengths of the remaining intervals is Conclude that the sum of the lengths of these intervals tends to 0 as n → ∞o.

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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Question

8. Show that, at the n stage of the construction of the Cantor Middle-
Thirds set, the sum of the lengths of the remaining intervals is
1
i=0
Conclude that the sum of the lengths of these intervals tends to 0 as n o.

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