The simple limit argument is justified because S(x) is monotonically increasing as x --> 1 from below along the real axis. This is clear by grouping the terms of the series as S(x) = (x - x^2) + (x^4 - x^8) + ... . Without some restriction on the path, the limit does not exist. The same grouping of terms shows that S(x) diverges to infinity when x --> w (w being a cube root of 1) along a line from the origin. Hence S(x) must also diverge to infinity along the line to exp(i t) with t of the form t = t[n] = (2 pi)/(3 2^n). Thus there exists a sequence of points x[n] --> 1, with arg(x[n]) = t[n] such that S(x[n]) --> infinity. Gene __________________________________ Do you Yahoo!? Yahoo! Mail - Helps protect you from nasty viruses. http://promotions.yahoo.com/new_mail