A square is drawn by joining mid pint of the sides of a square. Another square is drawn inside the second square in the same way and the process is continued in definitely. If the side of the first square is 16 cm, then what is the sum of the areas of all the squares ?

Explanation

To find the sum of the areas of all the squares formed by joining the midpoints of the sides of the previous square indefinitely, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the side length of the first square**:
The side length of the first square (let's call it \( S_1 \)) is given as 16 cm.

2. **Calculate the area of the first square**:
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