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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: 103,691

Hi;

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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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...

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

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...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,691

Hi n872yt3r;

7^2 = 49 and 10^2 = 100

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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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: 7,548

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

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