二、解的敛散性 1.由达氏判 R=lim k→∞ k+1 k+2 lim (k+2)(k+1) (+1)-k(k+1 x<1收敛 x>1发散 ④)当 x=1收敛?发散?
二、解的敛散性 1.由达氏判 1 2 lim lim k k k k k k a c R ®¥ a c ®¥ + + = = ( ) ( )( ) ( ) ( ) 3 2 1 lim 1 k 1 - 1 k k ®¥ l l k k + + = = + + ∴y(x)当 x < 1 收敛 x > 1 发散 x = 1 收敛 发? 散?
2.由高斯判 ReH>1收敛 则Σ/当 ReH≤1发散 将x=代入(6)和(7)得: y(1)=c2+cn();cn c2/—常数
2.由高斯判 1 k k f ¥ = 则å 当 Re 1 m > 收敛 Re 1 m £ 发散 将x = ±1代入 和 (6) (7 : )得 ( ) ( ) 2 0 0 2 2 0 1 1 1 , n n n n y c c c c ¥ = ± = + å ± ¬ 0 0 n n n c f f ¥ = = å 一常数