# Does the Sum Converge?

Calculus Level 3

Let $$\theta_k$$ be a randomly generated real number which varies with $$k$$. Does the following sum converge?

$\Large \sum^\infty_{k=0}\left(\frac{4}{3}\right)^{k} \, e^{(-\frac{k}{3} + i \theta_k)}$

 Notation: $$i=\sqrt{-1}$$ denotes the imaginary unit.

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