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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 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 . Convergent? ex. n ! n n . 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 ex. sin n n 2 7 Theorem: f r n g is convergent if 1 r 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 . Convergent? If so, nd the limit Tonights Homework: work out sequence problems. 8...
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This note was uploaded on 02/14/2012 for the course MAC 2312 taught by Professor Bonner during the Spring '08 term at University of Florida.
 Spring '08
 Bonner
 Calculus

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