Unformatted text preview: and ∑ b n converges and ∑ b n diverges Ratio Calculate a n has z n Yes, if ρ < 1 Yes, if ρ > 1 a n = 3 n n ! , test lim n →∞ a n +1 a n = ρ and/or n ! in it power series Root Calculate a n has z n , or f ( n ) n Yes, if ρ < 1 Yes, if ρ > 1 a n = 2 n 3 n n n test lim n →∞ a 1 n n = ρ Also, n 1 n → 1 Alternating Show u n +1 ≤ u n Whenever you see Yes, if the three. No a n = (1) n 3 n 2 n 3 +1 series test u n ≥ 0 and u n → ( − 1) n or ( − z ) n conditions are met. Check for absolute or conditional convergence. 1...
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This note was uploaded on 08/08/2008 for the course MATH 222 taught by Professor Wilson during the Fall '08 term at University of Wisconsin.
 Fall '08
 Wilson
 Calculus

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