The value of `1 div [1 div 1 div{1 div 1 div (1 div 1 div 2)}]` is

Options

A. 1
B. `5/8`
C. 2
D. `1/2`

Answer

To solve the expression \( 1 \div [1 \div 1 \div (1 \div 1 \div (1 \div 1 \div 2))] \), we will follow the order of operations, specifically focusing on the innermost brackets first.

### Step-by-Step Solution:

1. **Start with the innermost expression**:
\[ 1 \div 1 \div 2 \]
- Here, we first divide \( 1 \div 1 \) which equals \( 1 \).
- Now we have:
\[ 1 \div 2 = \frac{1}{2} \]

2. **Substitute back into the next outer expression**:
\[ 1 \div 1 \div \left(\frac{1}{2}\right) \]
- Again, we first divide \( 1 \div 1 \) which equals \( 1 \).
- Now we have:
\[ 1 \div \left(\frac{1}{2}\right) = 1 \times 2 = 2 \]

3. **Substitute back into the next outer expression**:
\[ 1 \div 1 \div 2 \]
- Again, we first divide \( 1 \div 1 \) which equals \( 1 \).
- Now we have:
\[ 1 \div 2 = \frac{1}{2} \]

4. **Substitute back into the outermost expression**:
\[ 1 \div \left(\frac{1}{2}\right) \]
- Finally, we have:
\[ 1 \div \left(\frac{1}{2}\right) = 1 \times 2 = 2 \]

### Final Answer:
The value of the expression \( 1 \div [1 \div 1 \div (1 \div 1 \div (1 \div 1 \div 2))] \) is \( 2 \).

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