Determine distribution, Prove Laplace Transform

Consider a game in which a fair coin is tossed indefinitely. Every time heads appears you move 1 metre to the right, and if tails you stay where you are. You start at position 0. Let be the number of tosses needed to first enter position n.

By definition

Determine the distribution of and prove that the Laplace Transform of is

Re: Determine distribution, Prove Laplace Transform

This question really intrigues me, I understand to find the Laplace Transform of Tn, you integrate Tn x exp(-st) from the limits of infinity to zero { ∫∞^0 T n × e^(-st) }Please excuse the bad formatting. But based on this question I am confused as to how to find the function of Tn. Could someone please explain?

Thanks