Question

A square T-2 is formed by joining the midpoints of another square T-1 of side 16cm. A third sqaure T-3 is fromed by joining the midpoints of another square T-2. Find sum of areas of all sqaure (including T-1) formed by repeating this process indefinitely.(in sq cm)

Answer 1

16^2 + 8^2 + 4^2 + 2^2 +...........

2^8 + 2^6 + 2^4 +...........

Now this is a GP or Geometric Progression

and sum till infinte terms of a GP is a/(1-r)

2^8/(1-2^{-2})

2^8/3/4

2^10/3 cm sq.

Thanks a lot

Please mark me as brainliest