Oops  this is Homework Help. I had fun working out the inductive equations and their general solution, but I suppose I shouldn't post all that here. So I stand by the previous suggestion that N+1 heads in a row takes N heads in a row plus one more, and then you may be done or you may need to start over. To check your work, I get 2001.6 for p = 0.73 and N = 20.
