A man starts going for morning walk every day. The distance walked by him on the first day was 2 kms. Everyday he walks half of the distance walked on the previous day. What can be the maximum total distance walked by him in his life time?

Options

A. 4kms
B. 120kms
C. 18kms
D. data inadequate

Answer

To find the maximum total distance walked by the man in his lifetime, we can analyze the pattern of distances he walks each day.

### Step-by-Step Solution:

1. **Identify the Distance on Each Day**:
- On the first day, the man walks 2 km.
- On the second day, he walks half of the distance of the first day:
\[ \text{Distance on Day 2} = \frac{2}{2} = 1 \text{ km} \]
- On the third day, he walks half of the distance of the second day:
\[ \text{Distance on Day 3} = \frac{1}{2} = 0.5 \text{ km} \]
- On the fourth day, he walks half of the distance of the third day:
\[ \text{Distance on Day 4} = \frac{0.5}{2} = 0.25 \text{ km} \]
- This pattern continues indefinitely.

2. **Formulate the Series**:
- The total distance walked can be expressed as an infinite series:
\[ \text{Total Distance} = 2 + 1 + 0.5 + 0.25 + \ldots \]

3. **Identify the Type of Series**:
- This series is a geometric series where:
- The first term \( a = 2 \)
- The common ratio \( r = \frac{1}{2} \)

4. **Use the Formula for the Sum of an Infinite Geometric Series**:
- The sum \( S \) of an infinite geometric series can be calculated using the formula:
\[ S = \frac{a}{1 - r} \]
- Substituting the values:
\[ S = \frac{2}{1 - \frac{1}{2}} = \frac{2}{\frac{1}{2}} = 2 \times 2 = 4 \text{ km} \]

5. **Conclusion**:
- The maximum total distance that the man can walk in his lifetime is **4 km**.