Convergence of alternating series
Posted: Tue Apr 25, 2017 7:16 am
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.
Prove that the series
$$\mathcal{S} = \sum_{n=1}^{\infty} \frac{(-1)^{n-1} |\sin n|}{n}$$
converges but not absolutely.