5.求幂级数∑ x"的和函数，并计算极限 n= s27…月 解：= 两边对x求导有 1-x) (1-x)2 x<1 lim 32月）- n-→0 lim ( ) 1 1 1 1 1 2 4 8 2 5. , lim 3 9 27 3 n n n n n nx  = →            求幂级数 的和函数 并计算极限 解： 两边对x求导有 1 1 n n x x x  = = −  1 2 1 1 (1 ) n n nx x  − = = −  2 1 1 (1 ) n n x nx x x  = =  −  ( ) 1 1 1 1 1 1 1 1 2 3 2 4 2 8 2 4 8 2 lim 3 9 27 3 lim 3 n n n n n n + + + + → →         =   1 1 1 1 1 1 ( ) lim ( 2 3 ) 2 2 4 8 2 3 3 n n n n n n  →  = + + + +  = = 2 1 2 1 (1 ) 2 3 9 − = =