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Unformatted text preview: f ( x ); be sure to check these 3 conditions ﬁrst: f ( x ) must be positive, continuous & decreasing. Alternating Series Test If ∞ X n =1 | a n | = ∞ X n =1 b n diverges, it is still possible for ∞ X n =1 (-1) n b n or ∞ X n =1 (-1) n-1 b n to converge conditionally . Remember to check both conditions necessary for convergence: lim n →∞ b n = 0 and b n +1 ≤ b n (decreasing). If All Else Fails Might need to look at partial sums S n = a 1 + ... + a n . For example, if the series is telescoping, computing ∞ X n =1 a n = lim n →∞ ( a 1 + ... + a n ) = lim n →∞ S n may be the only way to determine convergence (or divergence)....
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This note was uploaded on 09/21/2009 for the course MATH 1234 taught by Professor Egcdd during the Spring '09 term at Aarhus Universitet.
- Spring '09
- Geometric Series