| Exam Board | SPS |
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| Module | SPS FM (SPS FM) |
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| Year | 2021 |
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| Session | November |
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| Topic | Sequences and series, recurrence and convergence |
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9. (a) Show that
$$\frac { 1 } { 9 r - 4 } - \frac { 1 } { 9 r + 5 } = \frac { 9 } { ( 9 r - 4 ) ( 9 r + 5 ) }$$
(b) Hence use the method of differences to find
$$\sum _ { r = 1 } ^ { n } \frac { 1 } { ( 9 r - 4 ) ( 9 r + 5 ) }$$
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