Series convergence
Posted: Sun Apr 16, 2017 4:35 pm
Let $\{a_n\}_{n \in \mathbb{N}}$ be a sequence of positive real number such that $\sum \limits_{n=1}^{\infty} a_n$ converges. Is the series
$$\mathcal{S} = \sum_{n=1}^{\infty} n a_n \sin \frac{1}{n}$$
also convergent? Give a brief explanation.
$$\mathcal{S} = \sum_{n=1}^{\infty} n a_n \sin \frac{1}{n}$$
also convergent? Give a brief explanation.