| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2022 |
| Session | February |
| Marks | 7 |
| Topic | Partial Fractions |
| Type | Two linear factors in denominator |
| Difficulty | Moderate -0.3 Part (a) is a routine partial fractions decomposition with linear factors. Part (b) requires recognizing a telescoping series, which is a standard Further Maths technique, but the algebraic manipulation to express the final result as a single fraction adds minor complexity. Overall, this is a straightforward textbook exercise testing standard methods with no novel insight required. |
| Spec | 1.02y Partial fractions: decompose rational functions4.06b Method of differences: telescoping series |
\begin{enumerate}[label=(\alph*)]
\item Express $\frac{1}{(2r-1)(2r+1)}$ in partial fractions. [3]
\item Hence find $\sum_{r=1}^{n}\frac{1}{(2r-1)(2r+1)}$, expressing the result as a single fraction. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Pure 2022 Q1 [7]}}