- #1
C.E
- 102
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1. Let a_n be a sequence in R. Define [tex]\limsup_{n \to \infty} a_n[/tex]. Explain why it exists including the cases when the sequence is unbounded.
3. I did the following, is it ok?
definition:
[tex]\limsup_{n \to \infty} a_n[/tex]=[tex]\lim_{n \to \infty} sup_{k \geq n}a_k[/tex].
Is this right, I seem to have lost this part of my notes!
I know that when it is not bounded (above) the limsup is infinite. What I am really having
trouble with is explaining why it exists. What do you think they want me to say? (By the
way this question was worth 10 marks so they want a lot of detail).
3. I did the following, is it ok?
definition:
[tex]\limsup_{n \to \infty} a_n[/tex]=[tex]\lim_{n \to \infty} sup_{k \geq n}a_k[/tex].
Is this right, I seem to have lost this part of my notes!
I know that when it is not bounded (above) the limsup is infinite. What I am really having
trouble with is explaining why it exists. What do you think they want me to say? (By the
way this question was worth 10 marks so they want a lot of detail).