Riddles, brain puzzles and mathematical problems

[BAndrew]

Peter goes to Japan for business and needs to stay in a hotel for a week (7 days). He eventually finds one and decides to stay there. After a while trouble begins! The inn keeper doesn't accept dollars $ as payment. However he notices that Peter has a nice expensive golden chain with 7 links. He tells Peter that he can stay in the hotel if he gives him the chain instead for money (1 link per night). However there is a problem. The inn keeper demands to be paid every night. Peter can't give the full chain at the end of the week or pay in advance for other days. One night in the hotel costs exactly 1 link from Peter's chain. The inn keeper also wants Peter to cut/remove only one link from the chain to minimize damage. Peter thinks for a while and figures it out! How is he going to pay?