|f(tw)|→+∞\vert f(tw)\vert \rightarrow +\infty as t→1t\rightarrow 1 where f(z)=∑∞n=1zn!f(z)=\sum_{n=1}^{\infty}z^{n!} [on hold]

The power series ∑∞n=1zn!\sum_{n=1}^{\infty}z^{n!} has radius of convergence R=1R=1, so the function f(z)=∑∞n=1zn!f(z)=\sum_{n=1}^{\infty}z^{n!} is analytic on BR(0)B_R(0). Let w∈Cw\in\mathbb{C} be a root of unity. Show that |f(tw)|→+∞\vert f(tw)\vert\rightarrow +\infty as t→R−t\rightarrow R^{-}.

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