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# Geometric Series : Infinite Series of Circles inside Squares and Equilateral Triangles

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A circle of radius 100is inscribed in a square. The inscribing process continues to infinity. What is the sum of the unshaded areas?

Side of square 1 =________, Side of square 2 = __________, Side of square 3 = ___________Side of square 4 = ______________

Area of Circle 1 = ___________, Area of Circle 2 = _________, Area of Circle 3 = _____________Area of Circle 4 = _______________________
Area of Square 1 =_____________Area of Square 2 = ___________Area of Square 3=___________Area of Square 4 = _____________
Difference of 1st -_____________Difference of 2nd -________Difference of 3rd - ___________Difference of 4th - _______________

The next is same as above, but the circle with radius 100 is inscribed in an equilateral traiangle. The inscribing process continues until infinity. What is the sum of the unshaded area? All the above for this problem same as above.

https://brainmass.com/math/circles/infinite-series-circles-inside-squares-equilateral-triangle-40916

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A circle of radius 100is inscribed in a square. The inscribing process continues to infinity. What is the sum of the unshaded areas?

See a graph above. For two circles and squares, we have the relation between the side x and radius r. Obviously, for the square and its inscribed circle, x=2r.

For two circles, their radius have a relation as follows.