Something around the number
lim n 1 x1 n xn e. Since xn is arbitrary chosen so that it goes infinity, we finally obtain that lim x 1 1x x (3) In order to show 1 1 x x e as x,weletx y, then 1 1x x 1 1y y y y 1 y 1 1 y 1 y 1 1 1 y 1 Note that x y, by (6), we have shown that e lim y