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Is there a way to perform the finite sum $\sum_{m = 1}^n \exp(2 \pi i k (\sqrt5) ^m)$?, m even.

I am trying to show a specific sequence is not equidistributed, and so I'd like to show that Weyl's criterion fails, but I am not sure how to perform this sum, since it is not a geometric series.

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    Currently your index does not appear in your summand. Did you mean to write $$\sum_{k=1}^{n}\exp\left(2\pi i k(\sqrt{5})^n\right)$$ rather than $$\sum_{m=1}^{n}\exp\left(2\pi i k(\sqrt{5})^n\right)$$?2012-03-26
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    Yes, that is what I meant.2012-03-26
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    I am confused. Are you trying to evaluate $$\sum_{m=1}^{n}\exp(2\pi i k(\sqrt{5})^m)$$ or $$\sum_{k=1}^{n}\exp(2\pi i k(\sqrt{5})^n)$$. You just stated it was the latter that you meant, yet your edit provides the former as the series you intend. Also, if $m$ must be even, your series cannot begin at $1$.2012-03-26
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    Right, ack. I've edited the post. It's the first thing you typed,and m should start at 2.2012-03-26
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    Maybe you could just tell us what sequence is the one whose distribution you are investigating?2012-03-26

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