Why is this identity true? $$\sum_{k=1}^{\infty} \frac{\sin(k\pi/2)}{k^2} = G$$ where $G$ is Catalan's constant.
2026-03-29 04:42:54.1774759374
Sum of infinite series - Catalan constant
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The series sums to $$\frac{1}{1^2}-\frac{1}{3^2}+\frac{1}{5^2}-\cdots$$ which is just the definition of Catalan's constant.