2n+12 例2证明lim n)03n+23 证VE>0 2n+1 6n+3-6-4 3n+23 3(3n+2) 3(3n+2)(3n+2)n 令N=1,则当m>N时,有 E 2n+1 3n+23n例2 证明 ． 2 1 2 lim n 3 2 3 n →∞ n + = + 证 ∀ε >0 2 1 2 6 3 6 4 , 3 2 3 3(3 2) 1 1 1 3(3 2) (3 2) n n n n x a n n n n n + + − − − = − = + + = < < + + 令 N 1 , 则当 n>N 时，有 ε ⎡ ⎤ =⎢ ⎥ ⎣ ⎦ 2 1 2 1 . 3 2 3 n n x a n n ε + − = − < < +