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Unformatted text preview: (a) ∞ X n =1 3 n + 2 n 6 n ∞ X n =1 3 n + 2 n 6 n = ∞ X n =1 3 n 6 n + 2 n 6 n ! = ∞ X n =1 3 n 6 n + ∞ X n =1 2 n 6 n = ∞ X n =1 1 2 ! n + ∞ X n =1 1 3 ! n Since 1 2 < 1 and 1 3 < 1 the geometric series test tells us that the series converges. ∞ X n =1 1 2 ! 1 2 ! n1 + ∞ X n =1 1 3 ! 1 3 ! n1 = 1 / 2 11 / 2 + 1 / 3 11 / 3 = 1 + 1 2 = 3 2 (b) ∞ X n =1 1 5 n ∞ X n =1 1 5 n = 1 5 ∞ X n =1 1 n Since the Harmonic series diverges, this series also diverges....
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This note was uploaded on 07/11/2011 for the course MAC 2312 taught by Professor Bonner during the Spring '08 term at University of Florida.
 Spring '08
 Bonner

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