AQA FP2 — Question 1

Exam BoardAQA
ModuleFP2 (Further Pure Mathematics 2)
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TopicSequences and series, recurrence and convergence
1
  1. Show that $$\frac { 1 } { r ^ { 2 } } - \frac { 1 } { ( r + 1 ) ^ { 2 } } = \frac { 2 r + 1 } { r ^ { 2 } ( r + 1 ) ^ { 2 } }$$
  2. Hence find the sum of the first \(n\) terms of the series $$\frac { 3 } { 1 ^ { 2 } \times 2 ^ { 2 } } + \frac { 5 } { 2 ^ { 2 } \times 3 ^ { 2 } } + \frac { 7 } { 3 ^ { 2 } \times 4 ^ { 2 } } + \ldots$$
1 (a) Show that

$$\frac { 1 } { r ^ { 2 } } - \frac { 1 } { ( r + 1 ) ^ { 2 } } = \frac { 2 r + 1 } { r ^ { 2 } ( r + 1 ) ^ { 2 } }$$

(b) Hence find the sum of the first $n$ terms of the series

$$\frac { 3 } { 1 ^ { 2 } \times 2 ^ { 2 } } + \frac { 5 } { 2 ^ { 2 } \times 3 ^ { 2 } } + \frac { 7 } { 3 ^ { 2 } \times 4 ^ { 2 } } + \ldots$$

\hfill \mbox{\textit{AQA FP2  Q1}}
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