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(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}=

 

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


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Given series is ?n?114n2?1=?n?1un,say Then un=14n2?1,n ?1. Let {Sn} ba s
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