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#1 2013-01-30 13:55:32

3rdMath
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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

#2 2013-01-30 14:29:33

bobbym
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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.

#3 2013-01-30 22:45:13

n872yt3r
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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

#4 2013-01-31 01:20:27

anonimnystefy
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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...


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#5 2013-01-31 01:25:14

bobbym
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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.

#6 2013-01-31 02:51:26

mttal24
Member

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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

#7 2013-01-31 03:01:28

bob bundy
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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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