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JEE Main Mathematics question

MathematicsSequence and SeriesJEE Main

The length of a side of a square is "" metre. A second square is formed by joining the middle points of this square. Then a third square is formed by joining the middle points of the sides of the second square and so on. Then, the sum of the areas of the squares which carried upto infinity is

Answer: (B)

Solution

Joining the midpoints of the sides of a square gives a square of half the area, so the areas are . This is an infinite GP with first term and

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Question ID VK-021957