Question

Here’s a Sonic riddle! Sonic has the ability to jump forever. However, he gets a bit more tired after every jump, with each one going half as far as the previous. If the first jump takes him half a foot, the second a quarter of a foot and so on, how many jumps will it take for him to travel 1 foot?

Answer 1

Answer:

∞

Step-by-step explanation:

Given, the first jump takes him = 1/2 a foot,

           second jump takes him = 1/4 .

          thrid takes hime 1/8...and so on

         We can observe that  1/2, 1/4, 1/8 forms a geometric seuence with 1st term 1/2 and common ration 1/2.

  Let us assume that he takes 'n' jumps to travel 1 foot

  = Sum to nterms of given G.P = 1

   = a(1 - r^n)(1-r) = 1,

   => 1/2(1-1/2^n) = 1/2

  => 1/2^n =0

  => n tends to infinity,∞.