Unformatted text preview: log x and observe that x log x - x) = log x, so that
n k=1 n log k log n +
n k=1 1 n log x dx = log n + x log x - x) log x dx = x log x - x)
n , 1 n 1 , log k 1 As a result, we get 1 log n! 1 + log n (n/e)n for all n 1. The next result gives a better approximation to this fraction. Lemma 1.2 There exists a finite constant A 1 such that
n lim n! = A. n(n/e)n Remark 1.2.1 The previous lemma implies that n! A n(n/e)n as n ; in fact, one can show that A = 2. 1 O.H. Probability and Markov Chains MATH 256...
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This note was uploaded on 05/12/2010 for the course APPLIED ST 2010 taught by Professor Various during the Spring '10 term at Universidad Nacional Agraria La Molina.
- Spring '10