(b) {an}, where an 1 if n is odd and an = ; if n is even. |
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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Transcribed Image Text:In this problem, you do NOT have to do formal proofs. Feel free to use phrases like,
"We can see by inspection that sup A1 = 42."
For each of the following sequences {an}, define the set A, = {ar : k > n} and the
numbers s, = sup An and in = inf An as in the definition of lim sup and lim inf given
in Session 25. Give an explicit formula in terms of n for S, and in. (Your formula
may be piecewise-defined.) Determine lim sup a,n and lim inf a, and use your results
to determine whether {an} converges.
(b) {an}, where an = if n is odd and an = ; if n is even.
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