Chain links for lodging

A traveler wishes to stay at an inn for several days. He has no money, but he has a gold chain (like these o's joined together OOOOOOOO). The innkeeper agrees to let him stay on the condition that each day he pay one link of his chain. The traveler must pay every day; that is, at the end of one day, the innkeeper must have one link, at the end of two days, two links, at the end of three days, three links, and so forth. The traveler must cut his chain in order to make these payments. If the chain has seven links and the traveler stays for seven days, show how by cutting only one link he can pay for his lodging every day.