Question

A snail starts moving towards a point $3$cm away at a pace of $1$cm per hour. As it gets tired, it covers only half the distance compared to previous hour in each succeeding hour. In how much time will the snail reach his target?

Answer 1

The snail movement can be thought of that of a G.P.

$1,0.5,0.25,....$

$1+0.5+0.25+...=3$

$\frac{1-{0.5}^n}{1-0.5}=3$

$1-{0.5}^n=1.5$

${0.5}^n=-0.5$

which is not possible.Hence,it never reaches its target.