Suppose you and two other mathematicians are milling around thefood table before aseminar, eyeing the last four slices of cheese.How can you divide the four slices equallyamong the three ofyou?(a) Based on common sense, how much cheese should each of youget?5
(b) One of your mathematician friends suggests the followingsolution: “Let’s eachtake one of the slices of cheese, which leavesone slice for us to share. Instead ofcutting the remaining piece inthirds, let’s cut it into quarters, and each take aquarter of theleftover slice. We’re going to keep doing this, always cuttingtheremaining slice into quarters, taking a slice until there areonly crumbs too smallto be of interest to anyone. Sound good?”i.How much cheese will you have accrued after the third iteration?Fourth?Write the amount of cheese you will get via this process asan infinite sumusing sigma notation.ii. Based on your answer inpart (a) what can you say about the value of thesum in part i?
