Question 105

Let $$A_{1}$$ be a square whose side is a metres. Circle $$C_{1}$$ circumscribes the square $$A_{1}$$ such that all its vertices are on $$C_{1}$$. Another square $$A_{2}$$ circumscribes $$C_{1}$$. Circle $$C_{2}$$ circumscribes $$A_{2}$$, and $$A_{3}$$ circumscribes $$C_{2}$$, and so on. If $$D_{N}$$ is the area between the square $$A_{N}$$ and the circle $$C_{N}$$, where N is a natural number, then the ratio of the sum of all $$D_{N}$$ to $$D_{1}$$ is:

Solution

Is the condition for n = 2 and this will go on for higher values of n

as can be seen the area between square 1 and circle 1 is finite , square 2 and circle 2 is finite and so on

sum of all these areas for a higher value of n will become infinite

Therefore our answer is option 'C'

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