I am given the following function:
$f(z)=1+z^2+z^4+z^8+z^{16}+ \cdots$
and shall show that it is holomorphic in the unit disc, that $f\to\infty$ as $z\to e^{2i\pi/2^n}$, and that every point on the circle $|z|=1$ is singular. I struggle with the last part. It seems intuitive, since we are summing up different points on the circle that seem not to have any structure, but how can I show this?
thank you very much,
-m.p.