Unformatted text preview: +1 x n ± ± ± ± = L > 1 . Follow the steps (i)–(iii) below to prove that ( x n ) is unbounded, and hence divergent. (i) Prove that for any r < L , there is N r ∈ N such that ∀ n ≥ N , | x n +1 | > r | x n | . (ii) Fix a real r ∈ (1 ,L ) and let N r be as in part (a). Using mathematical induction prove that for all n ≥ N r , | x n | ≥ r n-N r | x N r | . (iii) Conclude that ( x n ) is unbounded, and hence divergent....
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- Spring '08
- Math, lim, elementary real analysis, nonzero reals, lim yn