c2 geometric series

Is it possible to draw this kind of diagram in the exam

Yes, all that is happening is the box is being cut in half repeatedly. You can imagine with additional cuts the image represents these summations:

1 cut: 1/2 + 1/2
2 cuts: 1/2 + 1/4 + 1/4
3 cuts: 1/2 + 1/4 + 1/8 + 1/8
4 cuts: 1/2 + 1/4 + 1/8 + 1/16 + 1/16
5 cuts: 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/32

etc..

which you should be able to see gets closer and closer to the series you are summing. Note that each and every one of those summations above total 1. Therefore the infinity version of the summation also comes to 1. This neat little trick is the reason why the graphic counts as a proof.

Drawing this should take no more than a minute.