| Exam Board | Edexcel |
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| Module | FP2 (Further Pure Mathematics 2) |
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| Year | 2003 |
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| Session | June |
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| Topic | Sequences and series, recurrence and convergence |
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4. (a) Express as a simplified single fraction \(\frac { 1 } { ( r - 1 ) ^ { 2 } } - \frac { 1 } { r ^ { 2 } }\).
(b) Hence prove, by the method of differences, that \(\quad \sum _ { r = 2 } ^ { n } \frac { 2 r - 1 } { r ^ { 2 } ( r - 1 ) ^ { 2 } } = 1 - \frac { 1 } { n ^ { 2 } }\).