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

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

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

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

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

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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**Yosef Bisk****Guest**

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