Let `S_1, S_2, ` be squares such that for each `ngeq1,` the length of a side of `S_n` equals the length of a diagonal of `S_(n+1)dot` If the length of a side of `S_1i s10c m ,` then for which of the following value of `n` is the area of `S_n` less than 1 sq. cm? a. 5 b. 7 c. 9 d. 10

Explanation

To solve the problem step by step, we need to analyze the relationship between the squares \( S_n \) and their areas.

### Step 1: Understanding the relationship between side length and diagonal
The length of the diagonal \( d \) of a square with side length \( s \) is given by the formula:
\[ d = s \sqrt{2} \]

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