Give an elementary proof that limn→∞:xn = 0 for 0 < x < 1. This means you are not allowed to use logarithms. Would you mind showing me the detail? Thank you so much for your help
Give an elementary proof that limn→∞:xn = 0 for 0 < x < 1. This means you are not allowed to use logarithms. Would you mind showing me the detail? Thank you so much for your help
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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Give an elementary proof that limn→∞:xn = 0 for 0 < x < 1. This means you are not allowed to use logarithms.
Would you mind showing me the detail? Thank you so much for your help
Transcribed Image Text:Hint: First show that the sequence Sn = x must converge, then determine that it converges to 0.
Expert Solution
Step 1
Here we use the limit definition of sequence to show its convergence as follows.
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