例5求lm( 2 十十 解:n-→>∞时,是无穷小之和 先变形再求极限 im(,+2,+…+1,)=lim 1+2+…+n n→)0 n(n+1) =lim im(1+)= n→0 n→0 2) 1 2 lim( 2 2 2 n n n n n + + + → 例5 求  解: n→时,是无穷小之和 先变形再求极限 ) 1 2 lim( 2 2 2 n n n n n + + + →  2 1 2 lim n n n + + + = →  2 ( 1) 2 1 lim n n n n + = → ) 1 (1 2 1 lim n n = + → 2 1 =