The total distance walked is given by the infinite series:
since distance has no sense of direction, only magnitude. Does this help?
A beetle starts at a point O on the floor. It walks 1m east, then 1/2m west, then 1/4m east and so on. How far it finish off O and how far did it actually walk?
Now here's my working:
We are given, ratio r = -(1/2), and first term a = 1 ... Since |r| < 1, it's a series that converges to a limit, so:
S = a / 1 - r
S = 1 / 1 - (-1/2) = 2/3
Therefore, the beetle ends up 2/3m from O.
Now ... I want help with how far did it actually walk. How should I go about calculating that?