How overdue can you safely go?

Sarah

I'm 40+1 and my doctor wants to induce me next Monday at 41 weeks if nothing happens by then . I tried to push for a little later but he didn't want to do that. How late can I really go safely? It seems like one week isn't that late.

I'm only 1cm 50% so he couldn't strip my membranes. Anyone have experience with going past due?