Unformatted text preview: < a < b . Prove b n +1a n +1 < ( n + 1) b n ( ba ). (c) Subsitute a = 1 + 1 n +1 and b = 1 + 1 n into the formula in part (b). Use this to show the sequence ( s n ) is increasing, i.e. s n +1 > s n for all n ≥ 1. (d) Prove that the subsequence of even terms is bounded by 4, i.e. ± 1 + 1 2 n ² 2 n ≤ 4 . Do this by plugging a = 1 and b = 1 + 1 2 n into the formula from part (b). Argue that since the sequence is increasing all terms must be bounded by 4. (e) Conclude the sequence converges, and denote its limit by e . (f) Find the limits of ± 1 + 1 2 n ² 2 n , ± 1 + 1 n ² 2 n , and ± 1 + 1 2 n ² n . 1...
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This note was uploaded on 10/16/2011 for the course MATH 34 taught by Professor Wiley during the Winter '11 term at UC Merced.
 Winter '11
 Wiley
 Differential Equations, Equations, Limits

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