Explanation:

The distance walked on the first day = 2 kms
The distance walked on subsequent days is half the distance walked on the previous days.
∴ Total distance walked
= 2 + 1 + 1/2 + 1/4 + ….
This is a Geometric series Whose First term, a = 2
common ratio, r = 1/2
Maximum total distance walked by the person in his lifetime
menas the number of terms in the series would be infinite.
Hence, the series would be an infinite Geometric series.
Sum of an infinite Geometric series is given by
S = a/(1 – r)
= S = 2/(1-1/2)
= S = 2/(1/2)
= s = 4 kms