Question

An insect is on the 0 point of a number line, hopping towards 1. She covers half the distance from her current location to 1 with each hop. So, she will be at `1/2` after one hop, `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 1^st hop = `1 - 1/2`

Distance covered in 2^nd hops = `1 - 1/4`

Distance covered in 3^rd hops = `1 - 1/8`

Distance covered in n hops = `1 - (1/2)^n`