3极限存在的充要条件 定理:设{A}={an+沥n},(n=1,…,A=a+沥 limb. =b n→o lim n 证(→): lim a=A n→0 n→00 vE>0,3N(E)>0,当n>N时,有A1-4<E TA -A=a, +ibm -a-ib=an-a+i(bm, -b an-a< -a+i(b-b)<8 bm-b<am-a+i(bn -b)<8{ } { },( 1,, ), , 定理: 设 A a ib n A a ib n n n = + = = +     = = → → lima a limb b n n n lim A A n n n = → 3 极限存在的充要条件 An A n lim = →     ,N( )  , n  N , A − A   0 0 当 时 有 n A A a i b a i b a a i( b b ) 而 n − = n + n − − = n − + n −  a − a  a − a + i( b − b )   n n n b − b  a − a + i( b − b )   n n n 证( ) 