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g.sreelatha

asked 2016-08-14 18:24:51

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

D. data inadequate

E. none

A. $4$ km

B. $2$ km

C. $8$ km

D. data inadequate

E. none

Javed Khan

answered 2016-08-14 18:45:24

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

$=\dfrac{2}{1-\dfrac{1}{2}}=\dfrac{2}{\left(\dfrac{1}{2}\right)}=4$

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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