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thedarktiger

Member

Registered: 2014-01-10

Posts: 91

infinite arithmetic series

heres the problem
(a)Determine all nonnegative integers r such that it is possible for an infinite arithmetic sequence to contain exactly r terms that are integers. Prove your answer.

seems like an awefull lot of cases

(b)Determine all nonnegative integers r such that it is possible for an infinite geometric sequence to contain exactly r terms that are integers. Prove your answer.

same thing

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Good. You can read.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: infinite arithmetic series

hi thedarktiger

Are there a lot of cases ?  I'm not so sure.

(a)  Let the first term be a and the difference be d.

Then the sequence is a, a+d, a + 2d, a + 3d, ......

If a and d are both integers, then every term will be an integer and we're not interested in those, as we want r to be a finite number.

So at least one of them must not be an integer.

If d is irrational then kd for all whole numbers, k, will be irrational.  So you'll only get a + kd to be an integer for one value of a.

If d is a proper fraction (ie. not whole) with denominator b , then an integer will pop up every time k = a multiple of b.  Once again, an infinite number of cases.

I think you can answer this question by considering cases like this.

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

Olinguito

Member

Registered: 2014-08-12

Posts: 649

Re: infinite arithmetic series

Last edited by Olinguito (2015-01-17 07:56:41)

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Bassaricyon neblina

thedarktiger

Member

Registered: 2014-01-10

Posts: 91

Re: infinite arithmetic series

How do you take down a post

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Good. You can read.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: infinite arithmetic series

Hi;

You mean delete this thread?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thedarktiger

Member

Registered: 2014-01-10

Posts: 91

Re: infinite arithmetic series

I just want to know how

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Good. You can read.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: infinite arithmetic series

At the bottom of each post you should see a delete button.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.