Question 11 - A-Level Maths

Edexcel FP2 2003 June — Question 11 7 marks

Exam Board	Edexcel
Module	FP2 (Further Pure Mathematics 2)
Year	2003
Session	June
Marks	7
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Partial Fractions
Type	Two linear factors in denominator
Difficulty	Standard +0.8 Part (a) is routine partial fractions with two linear factors. Part (b) requires recognizing telescoping series cancellation and then algebraic manipulation to reach the given form—this is non-trivial for A-level as it demands both the telescoping insight and careful algebraic verification, placing it moderately above average difficulty.
Spec	1.02y Partial fractions: decompose rational functions 4.06b Method of differences: telescoping series

11. (a) Express \(\frac { 2 } { ( r + 1 ) ( r + 3 ) }\) in partial fractions.
(b) Hence prove that \(\sum _ { r = 1 } ^ { n } \frac { 2 } { ( r + 1 ) ( r + 3 ) } \equiv \frac { n ( 5 n + 13 ) } { 6 ( n + 2 ) ( n + 3 ) }\).

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11. (a) Express $\frac { 2 } { ( r + 1 ) ( r + 3 ) }$ in partial fractions.\\
(b) Hence prove that $\sum _ { r = 1 } ^ { n } \frac { 2 } { ( r + 1 ) ( r + 3 ) } \equiv \frac { n ( 5 n + 13 ) } { 6 ( n + 2 ) ( n + 3 ) }$.\\

\hfill \mbox{\textit{Edexcel FP2 2003 Q11 [7]}}

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