workshop8

# workshop8 - Workshop 8 1 Each of the following sequences...

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Workshop 8 1) Each of the following sequences has limit 0: 1 n n =1 1 n n =1 1 n 2 n =1 1 10 n n =1 a) For each sequence, state exactly how large n must be to ensure that the term a n of the sequence (and all later terms as n increases) satisfy | a n | < 10 - 4 . b) Similarly, how large must n be to ensure that | a n | < 10 - 8 ? c) Use this information to explain which sequence approaches 0 most rapidly and which approaches 0 least rapidl 2) a) Two students are sharing a loaf of bread. Student Alpha eats half of the loaf, then student Beta eats half of what remains, then Alpha eats half of what remains, and so on. How much of the loaf will each student eat? b) Two students are sharing a loaf of bread. Student Alpha, now hungrier and more ferocious, eats two-thirds of the loaf, then student Beta eats eats half of what remains, then Alpha eats two-thirds of what remains, then Beta
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