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Geometric Progressions - Help please...

What is the sum of n terms of the following series:

a) x + 1 + 1/x + ...

b) 1 - y + y^2 - ...
Reply 1
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TeeEm
19
Original post by Abbie_D
What is the sum of n terms of the following series:

a) x + 1 + 1/x + ...

b) 1 - y + y^2 - ...


find the common ratio and use the summation formula
Reply 2
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Abbie_D
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Original post by TeeEm
find the common ratio and use the summation formula


Thanks for the reply. I have done but I still cannot get the exact answers. :confused:
Reply 3
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TeeEm
19
Original post by Abbie_D
Thanks for the reply. I have done but I still cannot get the exact answers. :confused:


post your working and I will try to point you in the right direction
Reply 4
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Abbie_D
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Original post by TeeEm
post your working and I will try to point you in the right direction


The answer is x^n-1/x^n-2(x-1)

My working so far:

Sn = x[(1/x)^n-1]/1/x-1
= x^n-1/1/x-1


:s-smilie:
Reply 5
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TeeEm
19
Original post by Abbie_D
The answer is x^n-1/x^n-2(x-1)

My working so far:

Sn = x[(1/x)^n-1]/1/x-1
= x^n-1/1/x-1


:s-smilie:


first line is fine

What is the answer meant to be, because the expression will be ugly no matter what
Reply 6
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Abbie_D
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Answer is: xn - 1 / xn-2(x-1)
Reply 7
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TeeEm
19
Original post by Abbie_D
Answer is: xn - 1 / xn-2(x-1)


can you see how to get your answer to that
Reply 8
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Abbie_D
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Original post by TeeEm
can you see how to get your answer to that


No, sorry :confused:
Reply 9
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TeeEm
19
Original post by Abbie_D
No, sorry :confused:


expand the bracket at the top
then multiply top and bottom by xn
(edited 9 years ago)
Reply 10
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Abbie_D
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Original post by TeeEm
expand the bracket at the top
then multiply top and bottom by xn+1


I'm still puzzled. Would it be possible if you could show your working to me please? :s-smilie:
Reply 11
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TeeEm
19
Original post by Abbie_D
I'm still puzzled. Would it be possible if you could show your working to me please? :s-smilie:


[x(1/xn - 1)]/[1/x-1]


=[1/xn-1 - x]/[1/x-1]

multiply to and bottom by xn-1
Reply 12
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Abbie_D
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Original post by TeeEm
[x(1/xn - 1)]/[1/x-1]


=[1/xn-1 - x]/[1/x-1]

multiply to and bottom by xn-1


I can understand up to: 1 - (x1 x xn-1 ) / xn-1 (1/x - 1)n
And I know how to get xn - 1 on the top, but how do you get the xn-2
(x-1) on the bottom?

I really appreciate your help by the way! :smile:
Reply 13
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TeeEm
19
Original post by Abbie_D
I can understand up to: 1 - (x1 x xn-1 ) / xn-1 (1/x - 1)n
And I know how to get xn - 1 on the top, but how do you get the xn-2
(x-1) on the bottom?

I really appreciate your help by the way! :smile:


the bottom should look

1/xn-1[1/x-1]


=1/xn-1 1/x[1 - x]

=1/xn-2[1 - x]
Reply 14
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Abbie_D
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Original post by TeeEm
the bottom should look

1/xn-1[1/x-1]


=1/xn-1 1/x[1 - x]

=1/xn-2[1 - x]


Thank you so much :smile:
Reply 15
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TeeEm
19
Original post by Abbie_D
Thank you so much :smile:


my pleasure

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