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The side of the large square is 1 unit and each black point divides its corresponding segment in half. If this blue area continues in this pattern, then what is the total area in blue?

 

 May 21, 2020
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So the largest blue square is 1/4 of the total.

 

The second largest is 1/4 of 1/4 of the total = 1/16

 

The third is (1/4)^3 = 1/64.

 

The fourth is (1/4)^4 = 1/256

 

The 2 fifths are 2* (1/4)^5 = 2*1/1024 = 1/512

 

We add these up giving

 

171/512

 

I'm not sure this is correct but pretty sure it is.

 

if you don't understand anything feel free to ask!

 May 21, 2020

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