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Unformatted text preview: MAT 132 Final Exam Review Sheet Section 8.1 A sequence is an ordered list of numbers. A series is the sum of an ordered list of numbers. Remember all of your rules of limits, but also remember when they dont apply. You only have lim n a n b n = lim n a n lim n b n if both limits exist. If either one doesnt exist, or is , then you cant do this. The same goes for sums, differences, and quotients. Remember the Squeeze Theorem - if a n b n c n and lim n a n = L = lim n c n , then lim n b n = L . Also remember the Monotonic Sequence Theorem - any bounded monotonic (which means always increasing or always decreasing) sequence is convergent. Section 8.2 A series S n = i =0 a i is convergent if lim n S n exists, where S n = n i =0 a i . These are called the partial sums. The series n =0 ar n is called the geometric series, and converges to a 1- r if r < 1. If r 1, it diverges. If a series n =0 a n converges, then lim n a n = 0. Notice that this only tells you that a series is divergent if the limit of the sequence isnt 0. If the limit of the sequence is 0, it could still be divergent....
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This note was uploaded on 01/13/2012 for the course MATH 2414 taught by Professor Mayfield during the Spring '09 term at Dallas Colleges.
- Spring '09