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.

Will the insect ever get to 1? Explain.

Answer 1

No, because for reaching `1, (1/2)^n` has to be zero for some finite n which is not possible.