Math Is Fun Forum

666 bro

Member

From: Flatland

Registered: 2019-04-26

Posts: 706

Sequences

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

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Sequences

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

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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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Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,974

Website

Re: Sequences

Hmm, it is hard to guess what the OP meant

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'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

Re: Sequences

Did you mean order in probability?

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