How can I show that $\sum_{n=1}^\infty (\sin n -\sin(πn/2)) / n^2$ converges or diverges? I tried using the ratio test but it's complicated I'd say it converges to $0$ since $n^2$ is growing faster than the numerator.
2026-04-02 17:41:28.1775151688
Series diverges or converges
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Hint : $$\left| \frac{\sin n-\sin(\pi n/2)}{n^2}\right|\le \frac{2}{n^2}$$
and use the fact 'Every absolutely convergent series is convergent.'