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**mrpace****Member**- Registered: 2012-08-16
- Posts: 54

n+1

(-1 )^(n-1) * 2n+1

what happens as n goes to infinity?

My thoughts are that it oscillates between near 0.5 and -0.5 but never hits either. does this mean it diverges?

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,531

Did you mean

When I first learnt about convergence, the implication was that if it didn't converge then it diverged. But, more recently, I have met a text that listed four possibilities:

converge, diverge, oscillate and periodic.

Putting a name to it, is not as important as describing what the sequence is doing.

Bob

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What is the difference between oscillating and periodic?

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**bob bundy****Moderator**- Registered: 2010-06-20
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oscillating: eg. 1, -1, 1, -1 ,1, -1, .............

periodic: eg. 1,2,3,5,1,2,3,5,1,2,3,5, ..........

I suppose you could argue that oscillating sequences are a special case of periodic.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

sin(n) would be oscillating, but not periodic.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,629

bob bundy wrote:

oscillating: eg. 1, -1, 1, -1 ,1, -1, .............

periodic: eg. 1,2,3,5,1,2,3,5,1,2,3,5, ..........

I suppose you could argue that oscillating sequences are a special case of periodic.

Bob

I thought it was the other way around.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

That sounds right. The only exception (that I can think of) is any constant sequence.

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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