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Unformatted text preview: , Â·Â·Â· = Â± 1 2 n1 Â² âˆž n =1 . lim n â†’âˆž a n = lim n â†’âˆž 1 2 n1 = lim n â†’âˆž Â³ 1 2 Â´ n1 = 0 since Âµ Âµ Âµ Âµ 1 2 Âµ Âµ Âµ Âµ < 1 . (b) lim n â†’âˆž 3 n 2 + 1 6 n 2 + 5 = lim n â†’âˆž 3 + 1 n 2 6 + 5 n 2 = 3 + 0 6 + 0 = 1 2 . 7. a n = 2 n +1 ( n + 1)! a n +1 a n = 2 n +2 ( n + 2)! Â· ( n + 1)! 2 n +1 = 2 n + 2 < 2 0 + 2 = 1 for all n â‰¥ 1 . Thus, Â± 2 n +1 ( n + 1)! Â² âˆž n =1 is strictly decreasing, and so, not strictly increasing....
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 Spring '08
 FRUGONI,ER
 Math

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