Vol. 5 No 10 - Pi Mu Epsilon

EULER'S CONSTANT AND EULER'S eThe sequence {adefined byna = x $-:nni=1can be shown to converge by demonstrating that the zequence is (1) de-creasing and (2) bounded below by 0. The value of this limit is oftenreferred to as EuZer's constant. Another constant associated with Euleris e. Euler introduced e to represent the base of the natural logarithm.One of the familiar properties of e is the following inequality:1 i 1 i+1(A) (1 + 7) < e < (1 + 7) , i = 1, 2, 3, .--.The purpose of this note is to show that by using (A), one can show thatthe above sequence (a 1 is convergent.nSince by (A)1 n+1e