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  4. Starting with a unit square, a sequence of square is generated. Each square in the sequence has half the side length of its predecessor and two of its sides bisected by its predecessor's sides as shown. This process is repeated indefinitely. The total area enclosed by all the squares in limiting situation, is

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Q. Starting with a unit square, a sequence of square is generated. Each square in the sequence has half the side length of its predecessor and two of its sides bisected by its predecessor's sides as shown. This process is repeated indefinitely. The total area enclosed by all the squares in limiting situation, isMathematics Question Image

Sequences and Series

Solution:

Required area $=1+\frac{3}{4}\left[\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^3}+\ldots \ldots \infty\right]=1+\frac{3}{4} \cdot \frac{\frac{1}{4}}{1-\frac{1}{4}}=1+\frac{1}{4}=\frac{5}{4} \Rightarrow( A )$