Infinity

In a square with side 18 is inscribed circle, in circle is inscribed next square, again circle and so on to infinity. Calculate the sum of area of all these squares.

Correct result:

S =  648

Solution:

$$\begin{gathered} {S}_1=18^2 \\ q={\displaystyle \frac{1}{2}},\mathrm{\mid }q\mathrm{\mid }<1 \\ S=S_1\cdot {\displaystyle \frac{1}{1-q}} \\ S=18^2\cdot {\displaystyle \frac{1}{1-{\displaystyle \frac{1}{2}}}}=648 \end{gathered}$$

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Showing 2 comments:

Ann

I don't believe this answer is correct. The ratio (q) to find the area of the next square should be 1/8, not 1/2.

6 months ago  Like

Math student

no it is 1/2

5 months ago  Like

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