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Geometric series

  • Thread starter nokia8650
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  • #1
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  • #2
tmc
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The sum that is done here is not the sum of the areas of every S_i; it is the sum whose result is the area of S_n itself. Look at A_3 in part (e), it is given as
A_3 = a^2 + 4a^2/9 + 4a^2/27
From this, you could guess that
A_4 = a^2 + 4a^2/9 + 4a^2/27 + 4a^2/81
And so on, such that A_n is such a sum. Every new term in the sum is the area of the extra little squares tacked onto the shape.
 
  • #3
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Hi, I understand that it is a geometric series, I was concerned with part (f). My question is why use the sum to infinity?

Thanks
 
  • #4
tiny-tim
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Hi, I understand that it is a geometric series, I was concerned with part (f). My question is why use the sum to infinity?
Hi nokia8650! :smile:

Because you want sup{Sn}, and the sequence is increasing, so you want S. :smile:
 
  • #5
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Thanks. The question says the sum to n, so shouldnt the equation be the sum ton, not the sum to inifnity?

Thanks
 
  • #6
tiny-tim
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Hi nokia8650! :smile:
Thanks. The question says the sum to n …
erm … no, it doesn't … it says "Find the smallest value of the constant S such that the area of Sn < S, for all values of n."

So you want sup{area of Sn}, which is the "area of S". :smile:
 
  • #7
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Thanks for the help. Its the wording of the question that is confusing me! So the question asks for the value of a constant which is greater than the area of the "final" square?

Thanks
 

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