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[tex] \sum^{\infty}_{n=0} p^{n}cos\left(n\theta\right) = \frac{1-pcos\theta}{1-2pcos\theta+p^{2}} [/tex]

if [tex] \left|p\right|<1[/tex].

Looking at this series, I see that p will approach zero as n approaches infinity, while the series oscillates because of the cosine term. The convergence is easy to see, but not the function that it converges to. The series is reminiscent of a geometric series, or possibly a Fourier series, but the cosine term really complicates things for me. I tried looking for similar problems on the web, but only found examples that apply the tests of convergence rather than determining this function.

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# Homework Help: Convergence of series of the form (r^n)cos(nx)

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