例15.利用夹逼定理证明 1).Iim/n=1;(2),Imn=0 证(1)令√n=1+x,则n=(1+x)y; nn 1) nn 而n=1+nx+ √2 →0<X →limr.=0 n-1 n→0 →iwn=im(1+xn)=1. n→0 H→0 证(2)√m"≤n!≤m"→ Wn n 而lim-=0,lim 0 n→0 n 0 →5n!3 例15. 利用夹逼定理证明 1 (1).lim 1; (2).lim 0 ! n n n n n → → n = = 1). 1 , (1 ) n n 证 n x n x = + = + n n ( 令 则 ； 2 2 ( 1) ( 1) 1 2! 2 n n n n n n n n n n nx x x x − − 而 = + + + +  2 2 2 0 lim 0 1 1 n n n n x x x n n →        = − − lim lim(1 ) 1. n n n n n x → →  = + = (2). ! n n 证 n n n    1 1 1 ! n n n n   1 1 lim 0, lim 0 n n → → n n 而 = = 1 lim 0 ! n n →  n  =