Standard +0.3 This is a standard method of differences question requiring partial fraction decomposition of 1/(n(n+2)), telescoping the series, and taking a limit. While it involves multiple steps, the technique is routine for Further Maths students and follows a well-practiced algorithm with no novel insight required.
2 Use the method of differences to find \(S _ { N }\), where
$$S _ { N } = \sum _ { n = 1 } ^ { N } \frac { 1 } { n ( n + 2 ) }$$
Deduce the value of \(\lim _ { N \rightarrow \infty } S _ { N }\).
2 Use the method of differences to find $S _ { N }$, where
$$S _ { N } = \sum _ { n = 1 } ^ { N } \frac { 1 } { n ( n + 2 ) }$$
Deduce the value of $\lim _ { N \rightarrow \infty } S _ { N }$.
\hfill \mbox{\textit{CAIE FP1 2010 Q2 [5]}}