If `S` denotes the sum to infinity and `S_n` the sum of `n` terms of the series `1+1/2+1/4+1/8+ ,` such that `S-S_n<1/(1000),` then the least value of `n` is `8` b. `9` c. `10` d. 11

Options

A. 8
B. 9
C. 10
D. 11

Explanation

To solve the problem, we need to find the least value of \( n \) such that the difference between the sum to infinity \( S \) and the sum of the first \( n \) terms \( S_n \) of the series \( 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \ldots \) is less than \( \frac{1}{1000} \).

### Step 1: Identify the series and its parameters
The series given is a geometric series where:
- The first term \( a = 1 \)
- The common ratio \( r = \frac{1}{2} \)

### Step 2: Calculate the sum to infinity \( S \)
...