Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**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?

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,393

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

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

Offline

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'

'Humanity is still kept intact. It remains within.' -Alokananda

**Online**

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,393

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

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

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

Offline

**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,532

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.

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

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

Offline

Pages: **1**