ON THE MONOTONY OF (1+1/n)^n+0.5 AND AN APPLICATION
Journal Title: Journal of Science And Arts - Year 2013, Vol 24, Issue 3
Abstract
In this paper we expose two different proofs for the fact that the sequence of general term (1+1/n^)n+0.5which convergesto the celebrated constant of Napier also called the number of Euler, the number e, is strictly decreasing. The one of the proofs shows the possibility of work without to use the differential calculus, the other is probably the most natural. We recall the situation of the monotony in the general case of (1+1/n)^n+p, we point out the order of convergence of (1+/n)^n+0.5 and we show how the monotony of the considered sequence can be used to obtain the shortest proof of the weak form of Stirling’s formul.
Authors and Affiliations
ANDREI VERNESCU
Keywords
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