Convergence of alternating series

Real Analysis
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Tolaso J Kos
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Convergence of alternating series

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Post by Tolaso J Kos »

The following series is an interesting one because of its slow convergence which you are asked to show! It was a question at École Polytechnique.

Prove that the series

$$\mathcal{S} = \sum_{n=1}^{\infty} \frac{(-1)^{n-1} |\sin n|}{n}$$

converges but not absolutely.
Imagination is much more important than knowledge.
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