| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2015 |
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| Session | June |
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| Topic | Proof by induction |
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3 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 \(\sum _ { r = 1 } ^ { \infty } \frac { 1 } { ( 2 r ) ^ { 2 } - 1 }\).