Just something that I couldn't think of an answer to.

Ok, say you start at 0 and are aiming for 10. The first second you take a 'step' of an amount (lets say 2), the second step you go half the previous amount (so 1), next step you half again (so .5) and so on. So you are always halving your previous step. So those three steps would take you from 2 to 3 and then to 3.5 etc.

As every step brings you closer to 10, if you continued this infinitely would you ever reach 10?

Also, does it make a difference what number you start with? I know that a number like 7 or 8 would bring you to 10 in the second step, but is there a rule like numbers over half the target number will eventually arrive there?

Thanks everyone.