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Results tagged with limits-and-convergence
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user 20598
Convergence of series, sequences and functions and different modes of convergence.
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Possible limits of $(1/n) \sum_{k=0}^{n-1} e^{i2\pi \cdot 2^k\alpha}$
I made a throwaway comment on math stackexchange the other day that got me thinking about the following question. Let
$$ f_n (\alpha) = \frac1n \sum_{k=0}^{n-1} e(2^k\alpha),$$
where $e(x) = \exp(i2\p …
- 9,720