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**3rdMath****Member**- Registered: 2013-01-29
- Posts: 1

Given the series 1/2 + 1/(2^4)+1/(2^7)+1/(2^10)

(i) show that this is geometric sequence..........can some1 help with this please

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,210

Hi;

That is a geometric series because each term has a common ratio which is

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**n872yt3r****Member**- Registered: 2013-01-21
- Posts: 392

(2^4=16) (2^7=49) (2^10=100) 1/16+1/49=0.0829081632653061224489795183673...+1/100=0.09290816326530612244897959183673...+1/2=0.59290816326530612244897959183673...

- n872yt3r

Math Is Fun Rocks!

By the power of the exponent, I square and cube you!

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,886

n872yt3r wrote:

(2^4=16) (2^7=49) (2^10=100) 1/16+1/49=0.0829081632653061224489795183673...+1/100=0.09290816326530612244897959183673...+1/2=0.59290816326530612244897959183673...

That is not correct. 2^7 is not 49 and 2^10 is not 100...

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 83,210

Hi n872yt3r;

7^2 = 49 and 10^2 = 100

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**mttal24****Member**- Registered: 2012-05-01
- Posts: 23

Well, to identify and prove a geometric progression the following can be used:

If

t2/t1=t3/t2=t4/t3=.....=tn/t(n-1)=r (and 'r' also represents common ratio)

then the sequence is a GP.

Here,

1/2^4 divided by1/2 is equal to 1/2^7 divided by 1/2^4.

Thus, you can show that it is a gp

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,269

hi 3rdMath

Welcome to the forum.

If you had an algebraic form for the general term, then you could do the job in one go with

As you have just 4 terms and no general term you will have to show that

The value for this constant has already been given in earlier posts.

Bob

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

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