Question

Let \( S_1 \) be a square of side 5 cm. Another square \( S_2 \) is drawn by joining midpoints of the sides of \( S_1 \). Square \( S_3 \) is drawn similarly and so on. Then \( \text{Area}(S_1) + \cdots + \text{Area}(S_{10}) \) is

• A. \(25\left(1-\frac{1}{2^{10}}\right)\)
• B. \(50\left(1-\frac{1}{2^{10}}\right)\)
• C. \(2\left(1-\frac{1}{2^{10}}\right)\)
• D. \(1-\frac{1}{2^{10}}\)
• E. \(10\left(1-\frac{1}{2^{10}}\right)\)

Hint:

Joining midpoints of a square always halves the area — remember this key geometric fact.

Answer 1

The Correct Option is B