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$ \sum_{n=1}^\infty \frac{\cos n \theta}{(\sqrt{13})^{n+1}}x^n $

Find the radius of convergence for the above series. I have learnt to use the root test and ratio test but neither of them seem to work. I have problems manipulating.

Not sure if this is useful: $\cos z = \frac{1}{2} \left(e^{iz}+e^{-iz} \right)$

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    @echoone what if $\theta$ is a complex number? In this case cosine is unbounded.2015-03-28

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Here is a hint. For any $N\in\mathbb{Z}^+$ we have that $\sup_{n>N}(\cos(n\theta))^{1/n} = 1$. Now try the root test.

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    @TheSubstitute yes.2015-04-02