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For a sequence (an), its lower and upper limits are defined by lim inf an = sup inf am = sup inf{an, an+1;•·· 1,...}, lim sup an = inf sup am = n m>n infsup{an, an+1,...}. n00 m>n n00

For a sequence (an), its lower and upper limits are defined by lim inf an = sup inf am = sup inf{an, an+1;•·· 1,...}, lim sup an = inf sup am = n m>n infsup{an, an+1,...}. n00 m>n n00

Advanced Engineering Mathematics
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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For a sequence (an), its lower and upper limits are defined by lim inf an = sup inf am = sup inf{an , An+1,· · ·}, m>n lim sup an = inf sup am = infsup{an, an+1, ...}. n00 n m>n n n n00 • Compute the lim inf and lim sup of the following two sequences: (-1)" bn 1+(-1)" + n An = sin n 2 • Show that lim inf an <lim sup an. n00 n00
Transcribed Image Text:For a sequence (an), its lower and upper limits are defined by lim inf an = sup inf am = sup inf{an , An+1,· · ·}, m>n lim sup an = inf sup am = infsup{an, an+1, ...}. n00 n m>n n n n00 • Compute the lim inf and lim sup of the following two sequences: (-1)" bn 1+(-1)" + n An = sin n 2 • Show that lim inf an <lim sup an. n00 n00
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