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Unformatted text preview: 1 √ n ( 1 √ n + 1√ n ) c ) lim n →∞ 1cos( n ) n d ) lim n →∞ ± 11 n 1 + 1 n ² n e ) lim n →∞ (11 √ n ) n III: (25 points) Consider the sequence, given recursively by a n +1 = 1(1a n ) 2 , a 1 = 1 2 . Is this sequence convergent? If yes calculate the limit. Proceed along the steps outlined below a) Is this sequence bounded above or below? b) Is this sequence monotone increasing or decreasing? c) Calculate the limit c . d) For which values of n is  ca n  < 106 ? IV: (25 points) Consider the recursively defned sequence a n +1 = 4 + 2 a 3 n 3 a 2 n , a 1 = 4 a) Show that this sequence is monotone decreasing and bounded below. b) Calculate its limit. c) Find a stopping rule N ( ε )....
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 Fall '08
 N/A
 Calculus, lim, recursively defined sequence, n→∞ n lim

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