注∵∑an=lim∑anx",求得S(x)=∑anx", =0 x→1 =0 =0 ∑n=lims(x)(逐项积分、逐项求导 =0 2n-1 例5求∑ 2n的和 2n-1 解令(x)=∑ 2n-2 2 上一页下一页返回lim ( ). 1 0 a s x x n n → −  =  = (逐项积分、逐项求导) lim , 0 1 0 n n n x n an a x  → =  = −  = ( ) , 0 n n s x an x  = 注 求得 = 例5   = − 1 2 2 1 n n n 求 的和 解 , 2 2 1 ( ) 2 2 1 −  =  − = n n n x n s x 令 (− 2, 2)