An Athlete jumping - Math Riddle
An Athlete is jumping. However, every time 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 for her to travel 1 foot?
She will never get to the 1-foot mark because you keep adding smaller and smaller amounts!
We will find the maximum value of this process, when this is carried out infinite times.
This process goes like a Infinite GP, whose
First term,a = 1/2ft.
Common Ratio, r = 1/2ft.
Maximum value of this process is One Foot when the athlete jumps forever or Practically, she will never complete her 1 foot.
Hence, Athlete will never complete. her complete .
As shown in Number line, since we are taking half distance of the previous one.
Starting from 1/2 ft. ,and ending at 1 foot.
The value always tends towardd 1 but never reaches one.