Renu wants to sell her laptop for $4000. Narmada offers to buy it for $3000. Renu then splits the difference and asks for $3500. Narmada likewise splits the difference and makes a new offer of $3250.
(a) If the women continue this process (of asking prices and counteroffers), what will Narmada be willing to pay on her 5th offer? kth offer? kth offer, k ≥ 1?
(b) If the women continue this process (providing many, many new asking prices and counteroffers), what price will they approach?
(c) Suppose that Narmada was willing to buy the laptop for $3200. What should she have offered to pay Renu the first time?