例5求im(2+2+…+2) n n n 解n→∞时,是无限多个无穷小之和 先变形再求极限 12 n 1+2+…+n n-)02 +2+…+“2)=Ii 2 ● n n(n+ 1) 2 =im:(1+-)= n→0 n n→ n 2 上页例5 ). 1 2 lim( 2 2 2 n n n n n + + + → 求  解 n → 时,是无限多个无穷小之和． 2 2 2 2 1 2 ) lim 1 2 lim( n n n n n n n n + + + + + + = → →   2 ( 1) 2 1 lim n n n n + = → ) 1 (1 2 1 lim n n = + → . 2 1 = 先变形再求极限