Question
An insect starts from a point and travels in a straight path 1 mm in the first second and half of the distance covered in the previous second in the succeeding second. In what time would it reach a point 3 mm away from its starting point?
Solution
Let a mm be the distance travelled in the first second. Since the insect covers half the distance covered in the previous second in the succeeding second.
∴ Distances covered in various seconds are 
Let r be the common ratio
∴ 
Let 3 mm distance be covered in n seconds
∴ 
which is impossible for any value of n.
Hence, the insect would never reach a point 3 mm away from its starting point.
