Infinity Square

Calculus Level pending

Red square have equal side of 4 cm. There are infinite amount of square inside it. What's the sum of all perimeter of square excluding red one.

38.63 27.66 30.42 30.01

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Ariful Hoque by Ariful Hoque , 23, Bangladesh

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2 solutions

Mayank Garg
Sep 22, 2014

Taking the diameter of the circle as the side of the previous square, it will create a possibility to calculate the radius and side of each and every circle and square respectively. After that, the sum of perimeters will be the sum of infinite geometric series, ie 18 + 8×1.414 + 8 +…………… And so on. Thus orally calculating, it will be greater than 35, Thus option A

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Rifath Rahman
Oct 9, 2014

The sum of perimeters=4 * 4/(sqrt 2)+4 * 4/2+..............=4{(4/sqrt 2)+4/2+.....}=4[(4/sqrt 2)/{1-(1/sqrt 2)}] [Using Geometric Progression]=4(4+4 * sqrt 2)=16+16 * sqrt 2=38.63

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