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Unformatted text preview: e ) lim n →∞ (1 + 1 n ) n 2 III: (25 points) Defne the sequence a n +1 = n n + 1 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 its limit c . Hint: Calculate the frst ±ew terms a 2 , a 3 , a 4 in this sequence. e) Find a stopping rule, i.e., ±or any ε > fnd N ( ε ) so that  a nc  < ε ±or all n > N ( ε ) . IV: (25 points) Consider the sequence, given recursively by a n +1 = a n + 90 10 , a 1 = 5 . 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  < 106 ?...
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This note was uploaded on 02/07/2011 for the course MATH 1501 taught by Professor N/a during the Fall '08 term at Georgia Institute of Technology.
 Fall '08
 N/A
 Calculus, Approximation

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