Abstract
In this paper, we present the following new inequality of n! n! > root 2 pi n(n+1/2)e(-n+Sigma r=0 infinity{(2n+2r+1)tanh-1(1/2n+2r+1)-1}) n is an element of N. Also, we deduce that the approximation formula n! similar to root 2 pi n(n+1/2)e(-n+Sigma k=1m2-2k/2k+1 zeta(2k,n+1/2)) has rate of convergence equal to n(-2m-1) for m = 1, 2, 3, ... . Thus, we can choose the approximation formula that we want it convergence to n! by a known rate. [Mustafa A. OBAID. On some lower bounds and approximation formulas for n! Life Sci J 2012;9(3):743-] (ISSN:1097-8135). http://www.lifesciencesite.com. 105