9231 P13 - Jun 2015 - Q3 - 7 marks
6294
Prove by mathematical induction that, for all positive integers \(n, \sum_{r=1}^{n} \frac{1}{(2 r)^{2}-1}=\frac{n}{2 n+1}\).
State the value of \(\sum_{r=1}^{\infty} \frac{1}{(2 r)^{2}-1}\).
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