The following equations a|<|a.-a+b.-b bn-b≤{xn-a|≤n-al+1-b → TH4.1.1 Complex series am=a, +ibn)(n=1, 2,converges toa=+iban→ a and b→b(n→∞) That is lima =a=atib iff lim a =a and lim b=b n→ n→>00 n→00Thefollowingequations n n n n n n n n a a a a b b b b a a b b     −  −  − + − −  −  − + −  TH 4.1.1    ( ) ( ) Complex series = =1,2,..., converges to = and . That is lim iff lim and lim . n n n n n n n n n n n a ib n a ib a a b b n a ib a a b b     → → → + +  → → →  = = + = =