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## #1 2007-02-12 08:59:58

woodoo
Member
Registered: 2007-02-10
Posts: 11

### Unbounded sequence that doesnt diverge to -∞ or ∞

I have a question that says find an unbounded sequence that doesn't diverge to -∞  or ∞. I can't figure one out, I don't think it exists. Anyone know of one?

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## #2 2007-02-12 09:24:28

kylekatarn
Member
Registered: 2005-07-24
Posts: 445

### Re: Unbounded sequence that doesnt diverge to -∞ or ∞

hmm...
"Divergent" means "not convergent"... there are "oscillating" sequences that don't converge, like this one:

oscillates: 1, -1, 1, -1, ...

But divergent not for -oo or +oo and unbounded, I am not seeing any example...

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## #3 2007-02-12 10:23:39

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Unbounded sequence that doesnt diverge to -∞ or ∞

I'd agree with that. If it doesn't diverge to infinity then it has to be bounded by some number, even if it's a million or something.

Why did the vector cross the road?
It wanted to be normal.

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## #4 2007-02-13 03:39:19

kylekatarn
Member
Registered: 2005-07-24
Posts: 445

### Re: Unbounded sequence that doesnt diverge to -∞ or ∞

a-ha!
but what can we say about:

* it's not convergent (oscillates around y=0)
* it's not bounded (fully or partially):

* yet it doesn't diverge either to +oo or -oo because:

Last edited by kylekatarn (2007-02-13 03:48:02)

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## #5 2007-02-13 04:16:23

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Unbounded sequence that doesnt diverge to -∞ or ∞

Interesting function, kylekatarn.  I've never thought of an unbounded sequence that had subsequences which one diverges to infinity and the other to negative infinity.

As for mine, I always stick with trig:

sin(n)

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #6 2013-12-14 16:25:53

Yosef Bisk
Guest

### Re: Unbounded sequence that doesnt diverge to -∞ or ∞

The sequence sin(n) is bounded within [-1,1] , perhaps you mean n(sin(n)) which does not diverge to + or - infinity but oscillates between positive and negative, and increases in absolute value