11.1 and 11.2 notes_Thomas' Calc II

11.1 and 11.2 notes_Thomas' Calc II - 11.1 Sequences...

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Unformatted text preview: 11.1 Sequences Infinite Seq. def.--an infinite seq. of #s is a function whose domain is the set of + integers Converges, Diverges, Limit def.--the seq. {an} converges to # L if to every + number there corresponds an integer N such that for all n , n > N => |a n L | < If no such # L exists, then seq. {an} diverges. If {an} converges to L , we write lim n a n = L and call L the limit of the seq. Diverges to def.--the seq. {a n } diverges to if for every # M theres an integer N such that for all n larger than N , a n > M . If condition holds we write Lim n a n = or a n Similarly if for every # m theres an integer N such that for all n > N we have a n < m , then say {a n } diverges to - we write Lim n a n = - or a n - Theorem 1. Let {a n } and {b n } be seqs. of real #s and let A and B be real #s. If lim n a n = A and lim n b n = B then 1. Sum Rule: lim n (a n + b n ) = A + B. 2. Difference Rule: lim n (a n b n ) = A B. 3. Product Rule: lim n (a n b n ) = AB. 4. Constant Multiple Rule: lim n (kb n ) = kB....
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11.1 and 11.2 notes_Thomas' Calc II - 11.1 Sequences...

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