Math Is Fun Forum

ABC1234

Member

Registered: 2016-12-22

Posts: 20

Geometric Sequences

Please Help:

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.

Thank you in advance!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometric Sequences

Hi;

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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.

ABC1234

Member

Registered: 2016-12-22

Posts: 20

Re: Geometric Sequences

I don't really understand the above explanation either

ABC1234

Member

Registered: 2016-12-22

Posts: 20

Re: Geometric Sequences

I think that the only possible value of r is 0 though.  I'm not sure how to go about proving that though.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geometric Sequences

No. Another  possible value is 1.First term is 1 and common ratio a rational fraction like
1,4/5,16/25,64/125,.... etc.
0 is also correct like 1/3,2/9,4/27 .... which has 0 integers.

Last edited by thickhead (2017-01-27 17:11:59)

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