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Unformatted text preview: lim n !1 b n lim n !1 ca n = c lim n ± > 1 a n (lim c = c ) lim n !1 a n b n = lim n !1 a n lim n !1 b n lim n !1 a n b n = lim n !1 a n lim n !1 b n ; lim n !1 b n 6 = 0 lim n !1 ( a n ) p = ( lim n !1 a n ) p ;p > ;a n > 5 Squeeze Theorem: If a n ± b n ± c n (for n ² n ) and lim a n = lim c n = L , then lim b n = L . Determine if each sequence is convergent, if so, ±nd the limit: ex. ± cos 2 n 2 n ² . Convergent? ex. ± n ! n n ² . Convergent? 6 Absolute Convergence Thm: If lim j a n j = 0 ; then lim a n = 0 : ex. ± ( ± 1) n ± 1 n n 2 + 1 ² ex. ± sin n n 2 ² 7 Theorem: f r n g is convergent if ± 1 ² r ² 1 ; divergent otherwise. lim n !1 r n = 8 > < > : if j r j < 1 1 if r = 1 divergent if j r j > 1 ex. f a n g = ± 2 n 3 n +1 ² . Convergent? If so, ±nd the limit Tonight’s Homework: work out sequence problems. 8...
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 Spring '08
 Bonner
 Calculus

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