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#1 2013-01-29 14:55:32

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

Geometric sequence

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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#2 2013-01-29 15:29:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,104

Re: Geometric sequence

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.
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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#3 2013-01-29 23:45:13

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

Re: Geometric sequence

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

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#4 2013-01-30 02:20:27

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,885

Re: Geometric sequence

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.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#5 2013-01-30 02:25:14

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 83,104

Re: Geometric sequence

Hi n872yt3r;

7^2 = 49 and 10^2 = 100


In mathematics, you don't understand things. You just get used to them.
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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#6 2013-01-30 03:51:26

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

Re: Geometric sequence

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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#7 2013-01-30 04:01:28

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

Re: Geometric sequence

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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