A square is drawn by joining the mid points of the sides of a given square in the same way and this process continues indefinitely. If a side of the first square is 4 cm, determine the sum of the areas all the square.
Choose the correct choice from the following options:
A) 32 cm 2	B) 16 cm 2	C) 20 cm 2	D) 64 cm 2	E) none of these

Rationale: solution : side of the first square is 4 cm . side of second square = 2 √ 2 cm . side of third square = 2 cm . and so on . i . e . 4 , 2 √ , 2 , √ 2 , 1 . . . . . . thus , area of these square will be , = 16 , 8 , 4 , 2 , 1 , 1 / 2 . . . . . . . hence , sum of the area of first , second , third square . . . . . . = 16 + 8 + 4 + 2 + 1 + . . . . . = [ 16 / { 1 - ( 1 / 2 ) } ] = 32 cm 2 . answer : option a
Answer: A