# Geometric series

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tmc
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.

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

tiny-tim
Homework Helper
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! Because you want sup{Sn}, and the sequence is increasing, so you want S. Thanks. The question says the sum to n, so shouldnt the equation be the sum ton, not the sum to inifnity?

Thanks

tiny-tim
Homework Helper
Hi nokia8650! 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". 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