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Unformatted text preview: to nd the limit lim n s n . By part (a) the sequence is bounded below and by part (b) the sequence is nonincreasing. Hence, by the Monotone Convergence Theorem, the sequence ( s n ) n converges. Let s denote the limit. We have by various algebraic limit theorems that s = lim n s n +1 = lim n 21 s n = lim n 2lim n 1 s n = 21 s . Hence, s = 21 s and so 0 = s 22 s + 1 = ( s1) 2 . It follows that lim n s n = 1....
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 Spring '08
 Katsuura,H
 Math, Calculus

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