ABCD is a square with area 9. efgc is a square in which EC=1/3(BC). HIJC is s square in which HC=1/3(EC). If this pattern is continued so that there are a total of ten squares with common vertex at C. and in which each square lies inside its predecessor, what is the area of the tenth square?
That answer is correct.
In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.
how to solve this problem. please explain!
ABCD has area 3 x 3 = 9 = 9 ^ 1
EFCG has area 1 x 1 = 1 = 9 ^ 0
HICJ has area 1/3 x 1/3 = 1/9 = 9 ^ -1
KLCM has area 1/9 x 1/9 = 1/81 = 9 ^ -2
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10th square has area 3^ -8 x 3 ^ -8 = 9 ^ -8
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