SOLUTION: hello unfortunatly I can't figure out this word problem and i REALLY need help! A Pythagorean fractal tree starts at Stage 1 with a square of side length 1m. At every consecutiv

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Question 117289: hello unfortunatly I can't figure out this word problem and i REALLY need help!
A Pythagorean fractal tree starts at Stage 1 with a square of side length 1m. At every consecutive stage, an isoceles right triangle and two squares are attached to the last square(s) drawn. Determine the total area at the 10th stage and the 100th stage. Determine the general term and make conclusions.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
I found only this for you:
Iteration n in the construction adds 2%5En squares of size %28%281%2F2%29sqrt%282%29%29%5E2n for a total area of 1.
Thus the area of the tree might seem to grow without bound in the limit
n+-%3Einfinity
However, some of the squares overlap starting at the order 5 iteration, and the tree actually has a finite+area because it fits inside a 6%2A4 box.
It can be shown easily that the area
A+of the Pythagoras+tree must be in the range
5+%3C+A+%3C18, which can be narrowed down further with extra effort.
Little seems to be known about the actual value of +A.
Let n=10
2%5E10%281%2F2%2Asqrt%282%29%29%5E20=1
2%5E10%28.5%2A1.4142%29%29%5E20=1
2%5E10%28.707%29%29%5E20=1

1024%28.707%29%5E20=1
1024%28.000976%29=1
1=1

Let n=100
2%5E100%281%2F2%2Asqrt%282%29%29%5E200=1
2%5E100%28.5%2A1.4142%29%29%5E200=1
2%5E100%28.707%29%29%5E200=1

1.2676%2A10%5E30%2A1.046%2A10%5E-31=1
1.3%2A10%5E30%2A1%2F%281.046%2A10%5E31%29=1
1.3%281%2F%281.046%2A10%29%29=1
1.3%2A.9+=1
1.17=1 ....1.17 could be rounded to 1

I hope it will help.