n=1 5. This question is about lim inf and lim sup. For a sequence (an) let in 8 = inf{a: k2n). Then lim inf a, lim i,, and lim supa, = lim 8- 81x Show that (i) may be too). Note: this proof in the text inf{ak 2n} and and (s) are monotone, so that lim inf and lim sup always exist (they This is essentially Theorem 2.6.1 from your text. You are welcome to look at (it is not complicated!) but put the proof in your own words. (For the sequence (; +1 terms of these sequences) and also compute lim inf and lim sup n+1 (-1)" Hint: Look at example 2.6.3 in 2" compute the sequences (in) and (8) = 0% (i.e. list the 1 n+1 -Compute lim inf(-1)" + and lim sup(-1)"+ your text. (-1)" 2
n=1 5. This question is about lim inf and lim sup. For a sequence (an) let in 8 = inf{a: k2n). Then lim inf a, lim i,, and lim supa, = lim 8- 81x Show that (i) may be too). Note: this proof in the text inf{ak 2n} and and (s) are monotone, so that lim inf and lim sup always exist (they This is essentially Theorem 2.6.1 from your text. You are welcome to look at (it is not complicated!) but put the proof in your own words. (For the sequence (; +1 terms of these sequences) and also compute lim inf and lim sup n+1 (-1)" Hint: Look at example 2.6.3 in 2" compute the sequences (in) and (8) = 0% (i.e. list the 1 n+1 -Compute lim inf(-1)" + and lim sup(-1)"+ your text. (-1)" 2
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:5. This question is about lim inf and lim sup. For a sequence (a)olet in = infla, kn) and
8n inf{ak k2n). Then lim inf an = lim in, and lim supa, = lim 8
71-8
Show that (i) and (s) are monotone, so that lim inf and lim sup always exist (they
may be too). Note: This is essentially Theorem 2.6.1 from your text. You are welcome to look at
this proof in the text (it is not complicated!) but put the proof in your own words.
1
+1
compute the sequences (in) and (8) = 0% (i.e. list the
1
1
terms of these sequences) and also compute lim inf and lim sup
n+1
n+1
and lim sup(-1)"+
For the sequence ;
(Compute lim inf(-1)" +
your text.
2"
(-1)"
2n
Hint: Look at example 2.6.3 in
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