| Exam Board | SPS |
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| Module | SPS FM (SPS FM) |
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| Year | 2020 |
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| Session | May |
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| Marks | 6 |
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| Topic | Sequences and series, recurrence and convergence |
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8.
Let
$$S _ { n } = \sum _ { r = 1 } ^ { n } \frac { 1 } { ( r + 1 ) ( r + 3 ) }$$
where \(n \geq 1\)
Use the method of differences to show that
$$S _ { n } = \frac { 5 n ^ { 2 } + a n } { 12 ( n + b ) ( n + c ) }$$
where \(a\), \(b\) and \(c\) are integers.
[0pt]
[6 marks]