2阿贝尔法(构造幂级数法): oo ∑an=im∑nx,求得s(x)=∑anx", n=0 =0 n=0 ∑an=lim(x).(逐项积分、逐项求导) n=0 x→ 工工工 例4求∑ 2n-1的和 2 解令(x)=∑2x2"2,(√2,2) n=1 上页2.阿贝尔法(构造幂级数法): lim , 0 1 0 n n n x n an a x  → =  = −  = ( ) , 0 n n s x an x  = 求得 = lim ( ). 1 0 a s x x n n → −  =  = (逐项积分、逐项求导) 例4 . 2 2 1 1 求  的和  = − n n n 解 , 2 2 1 ( ) 2 2 1 −  =  − = n n n x n 令 s x (− 2, 2)