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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 706

How would the limit of an sequence be oscillatory explain with an example?

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,408

I can think of two ways of interpreting this question. My first thought was

1, -1, 1, -1, 1, -1, ……..

The sum of terms oscillates between 1 and zero depending on whether you've reached an odd term or an even.

But then I thought: can you really refer to this as a limit if we're not getting closer and closer to a value?

Here's an example where the terms do tend to a limit but oscillating either side of that value:

1/1, 2/1, 3/2, 5/3, 8/5, 13/8, 21/13, …….

The numbers are successive numbers in the Fibonacci sequence (term r+2 is calculated by adding term r and term r+1) and tends to the golden ratio, 1.618....

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

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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Hmm, it is hard to guess what the OP meant

'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'

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**666 bro****Member**- From: Flatland
- Registered: 2019-04-26
- Posts: 706

Did you mean order in probability?

"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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