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## #1 2014-07-29 17:09:31

mrpace
Member
Registered: 2012-08-16
Posts: 77

### Does this sequence converge or diverge?

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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## #2 2014-07-29 20:23:57

bob bundy
Registered: 2010-06-20
Posts: 8,340

### Re: Does this sequence converge or diverge?

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

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #3 2014-07-30 00:34:03

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,851
Website

### Re: Does this sequence converge or diverge?

What is the difference between oscillating and periodic?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #4 2014-07-30 01:49:32

bob bundy
Registered: 2010-06-20
Posts: 8,340

### Re: Does this sequence converge or diverge?

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

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #5 2014-07-30 03:03:50

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Does this sequence converge or diverge?

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

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #6 2014-07-30 06:22:18

ShivamS
Member
Registered: 2011-02-07
Posts: 3,648

### Re: Does this sequence converge or diverge?

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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## #7 2014-07-30 10:00:45

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Does this sequence converge or diverge?

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

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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