If `S_n = 1+1/2 + 1/2^2+...+1/2^(n-1) and 2-S_n < 1/100,` then the least value of `n` must be :

Explanation

To solve the problem, we need to find the least value of \( n \) such that \( S_n = 1 + \frac{1}{2} + \frac{1}{2^2} + \ldots + \frac{1}{2^{n-1}} \) satisfies the condition \( 2 - S_n < \frac{1}{100} \).

### Step-by-Step Solution:

1. **Identify the Series**:
The series \( S_n \) is a geometric series where:
- First term \( a = 1 \)
- Common ratio \( r = \frac{1}{2} \)
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