An athlete us jumping. However, everytime she jumps she gets a bit more tired, and every jump goes 1/2 as far as her prior jump. Now, for her very first jump, she goes 1/2 of a foot. On her second jump, she goes 1/4 of a foot, and so on and so forth. How many jumps does it take to get to travel 1 foot

She can never travel a distance of 1 foot for the given condition.

Step-by-step explanation:

In every jump, she goes 1/2 as far as her prior jump.

In the 1st jump, she covered a distance, d_1= \frac 1 2 foot.

The distance covered in the 2nd jump

(given)

So, the distanve covered in the 3rd jump

Similarly, the distance covered in the jump

Assuming she requires jumps to travel 1 foot of distance.

So, the sum of all the distances covered in n jumps = 1 foot

This a geometric progression, G.P., of terms having common ration, r= 1/2 and the first term .

As sum of all the n terms of  G.P ,

This is only possible, mathematically, when , But in real life situation reaching infinity is not possible.

Hence, she can never travel a distance of 1 foot for the given condition.