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g.sreelatha
A man starts going for morning walk everyday. The distance walked by him on the first day was $2$ km, everyday he walks half of the distance walked on the distance walked on the previous day. What can be the maximum total distance walked by him in his lifetime?
A. $4$ km
B. $2$ km
C. $8$ km
E. none
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Javed Khan
Ans: $4$ km

First day: $2$ km
Second day: $1$ km
Third day: $\dfrac{1}{2}$ km
So on.

Total distance travelled
$=2+1+\dfrac{1}{2}+\cdots$

This is an infinite geometric progression with first term $2$ and common ratio $\dfrac{1}{2}$

Therefore, the above sum
$=\dfrac{2}{1-\dfrac{1}{2}}=\dfrac{2}{\left(\dfrac{1}{2}\right)}=4$
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