10 (i) You are given that

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

Use the method of differences to show that

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

(ii) Hence find the sum of the infinite series

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

RECOGNISING ACHIEVEMENT

\section*{OXFORD CAMBRIDGE AND RSA EXAMINATIONS}
\section*{Advanced Subsidiary General Certificate of Education Advanced General Certificate of Education}
\section*{MEI STRUCTURED MATHEMATICS}

Further Concepts For Advanced Mathematics (FP1)\\
Wednesday 18 JANUARY 2006 Afternoon ..... 1 hour 30 minutes\\
Additional materials:\\
8 page answer booklet\\
Graph paper\\
MEI Examination Formulae and Tables (MF2)

TIME 1 hour 30 minutes

\begin{itemize}
  \item Write your name, centre number and candidate number in the spaces provided on the answer booklet.
  \item Answer all the questions.
  \item You are permitted to use a graphical calculator in this paper.
  \item Final answers should be given to a degree of accuracy appropriate to the context.
\end{itemize}

\begin{itemize}
  \item The number of marks is given in brackets [ ] at the end of each question or part question.
  \item You are advised that an answer may receive no marks unless you show sufficient detail of the working to indicate that a correct method is being used.
  \item The total number of marks for this paper is 72.
\end{itemize}

\hfill \mbox{\textit{OCR MEI FP1  Q10}}