22n+1例3.求极限 lim[-(n+1)2)n→n+1n+2解：222n+12n+112n+1..+...+2n+1n+2(n+1)(n+1)2n2+1n+ln+1(n+1)2(n+1)222n+1(2n+1)(2n+2)1(2n+1)(2n+2)(n+1)2n+1n2+22(n+1)2(n+1)222n+12n+3n+1(2n+1)+·.+<(n+1)n2+1n2+2n+1n+1(2n+l)2n2+3n+1lim=2lim=2..n+1n?+1n-n>0022n+1liml=2由夹逼准则有(n+1)2n2+2n-n+1例3. 求极限 2 2 2 1 2 2 1 lim[ ]. 1 2 ( 1) n n →  n n n + + + + + + + 解： 2 2 2 1 2 2 1 + 1 2 ( 1) n n n n + + + + + + 2 2 2 1 2 2 1 + 1 1 1 n n n n +  + + + + + 2 2 2 1 2 2 1 + ( 1) ( 1) ( 1) n n n n + + +  + + +2 (2 1)(2 2) 2( 1) n n n + +  + 2 (2 1)(2 2) 2( 1) n n n + +  + 2 2 2 1 2 2 1 + 1 2 ( 1) n n n n + + + + + + (2 1) 1 n n +  + 2 2 2 3 1 1 n n n + +  + 2 2 2 1 2 2 1 + 1 2 ( 1) n n n n + + + + + + (2 1) lim 2 n 1 n → n +  = + 2 2 2 3 1 lim 2 n 1 n n → n + + = + 2 2 2 1 2 2 1 lim[ ] 2 1 2 ( 1) n n →  n n n + + + + = + + + 由夹逼准则有