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Unformatted text preview: -1 (4 / 5). What is the probability that heads is rst seen after an odd number of ips? THERE ARE MORE PROBLEMS ON THE BACK SIDE. Typeset by A M S-T E X 1 . 6.[20 points total] (i)[5 points] Let a 1 , a 2 , a 3 . . . be a sequence of real numbers, and suppose L is a real number. What is the denition for lim n a n = L ? (ii) For each of the following, write TRUE or FALSE. No justication need be provided. [3 points each] (a) R 1 ( 1 / x ) dx = . (b) If lim n a n = 0, then the series n =1 a n converges. (c) A sequence of real numbers a n is bounded if a n < 100 for every n . (d) If a sequence is bounded and increasing, then it converges to a real number. (e) lim n [(1 + 1 / 2 + 1 / 3 + + 1 /n )-ln( n )] = . 2...
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This note was uploaded on 04/03/2010 for the course MATH 20 taught by Professor Staff during the Fall '08 term at Maryland.
- Fall '08