(Solved):
b- Show that \( \sum_{n=1}^{\infty} \frac{1}{4 n^{2}-1}=\frac{1}{2} \) and \( \sum_{n=1}^{ ...
b- Show that \( \sum_{n=1}^{\infty} \frac{1}{4 n^{2}-1}=\frac{1}{2} \) and \( \sum_{n=1}^{\infty} \frac{(-1)^{n}}{4 n^{2}-1}=\frac{1}{2}-\frac{\pi}{4} \).