Question

Question 127(ii)

An insect is on the 0 point of a number line, hopping towards 1. It covers half the distance from its current location to 1 with each hop.
So, it will be at $\frac{1}{2}$ after one hop, $\frac{3}{4}$ after two hops and so on.



Where will the insect be after n hops?

Answer 1

If we see the distance covered in each hops
Distance covered in 1st hop = 1- $\frac{1}{2}$
$=1-{\left(\frac{1}{2}\right)}^1$
Distance covered in 2nd hop = 1 - $\frac{1}{4}$

$=1-{\left(\frac{1}{2}\right)}^2$
Distance covered in 3rd hop = 1 - $\frac{1}{8}$

$=1-{\left(\frac{1}{2}\right)}^3$

$..................$
Distance covered in n hops = 1 - ${\left(\frac{1}{2}\right)}^n$