例1.3.1求lim 2 n>n2+n+1n2+n+2 ntn+n 解 2 设S +n+1n2+n+2 n+n+n (n+1)1+2+…+n 1+2+…+nn(n+1) <.< 2(n2+2n) n +en n2+n+12(n2+n+1) .li n(n+D)=lim-+n+)2 n(n+1)1 2(n2+2n) lim s3 例1.3.1 求 2 2 2 1 2 lim n 1 2 n  n n n n n n n                解: 设 2 2 2 1 2 1 2 n n S n n n n n n n           2 2 2 2 ( 1) 1 2 1 2 ( 1) 2( 2 ) 2 1 2( 1) n n n n n n n S n n n n n n n n                   2 2 ( 1) ( 1) 1 lim lim n n 2( 2 ) 2( 1) 2 n n n n   n n n n        1 lim . 2 n n S   