方法二 n 2n+1 2n 收敛∴原级数收敛 lim -n+l=lim +X川+x 1-70 un n-p(1+x1+x2)-1+xn+ limX 0<x<1 X=1 ∴级数收敛 2 0 lim un+=limIn(n+1)2nVn n2时+√n+1lmn lir n(n+1)n+11 <0收敛 n-y 2Inn v n2 (3)当a=1 lim u=lim=≠0发散 n→0 0<a<1 li lim 1≠0发散 a>1 1 为公比-<1的等比级数 a a 收敛 (4)∵1im7 =lim 6 收敛 原级数收敛方法二: n n n 2 1 2n n 2n 1 n = + ∵ = n 1 n 2 1 收敛 ∴ 原级数收敛 ( )( ) ( ) ( )( ) ( ) n 2 n 2 n 1 n 1 n n n 1 n x 1 x 1 x 1 x 1 x 1 x 1 x x lim u u lim + + + + + + = + + → + → n 1 n 1 x x lim + → + = = = 0 x 1 x 1 2 1 x 0 x 1 ∴级数收敛 ( ) lnn 2 n 2 n 1 ln n 1 lim u u lim n n 1 n n n 1 n + + = → + + → ( ) 0 2 1 n n 1 2lnn ln n 1 lim n = + + = → 收敛 (3)当 0 2 1 2 1 a 1 lim u lim n n n = = = → → 发散 1 0 1 a 1 0 a 1 limu lim n n n n 0 = + = → → 发散 = + n 1 n n n a 1 a 1 1 a 1 a 1 为公比 1 a 1 的等比级数 ∴ 收敛 (4)∵ 1 7 5 7 lim 7 6 7 5 6 lim n n n n n n n n n n = − − = → → ∵ = n 1 n 7 6 收敛, ∴ 原级数收敛