I'm reading "Time Series Analysis and Its Applications with R examples", 3rd edition, by Shumway and Stoffer, and I don't really understand a proof. This is not for homework, just my own edification.(adsbygoogle = window.adsbygoogle || []).push({});

It goes like this:

Σ_{t=1}^{n}cos^{2}(2πtj/n) = ¼ ∑_{t=1}^{n}(e^{2πitj/n}- e^{2πitj/n})^{2}= ¼∑_{t=1}^{n}e^{4πtj/n}+ 1 + 1 + e^{-4πtj/n}= n/2.

I'm don't see how the last equality follows. I think, somehow, that the e^{4πtj/n}and e^{-4πtj/n}terms cancel out, but how?

Any ideas?

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# A Basic Spectral Analysis proof help

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