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Unformatted text preview: e ) lim n (1 + 1 n ) n III: (25 points) Defne the sequence a n +1 = n + 1 10 n a n , a 1 = 1 a) Find upper and lower bounds on this sequence. b) Is this sequence increasing or decreasing? c) Explain why the sequence is convergent. d) Calculate the limit c . Hint: Calculate the frst ew terms a 2 , a 3 , a 4 in this sequence. e) For which values o n is  a nc  < 1010 ? IV: (25 points) Consider the sequence, given recursively by a n +1 = a n + 20 10 , a 1 = 1 . Is this sequence convergent? If yes caculate the limit. Proceed along with 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  < 108 ?...
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 Fall '08
 N/A
 Calculus, Approximation

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