| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Partial Fractions |
| Type | Two linear factors in denominator |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question combining routine partial fractions with telescoping series. Part (a) is standard decomposition with two linear factors, and part (b) requires recognizing the telescoping pattern—a common FP2 technique. While it's Further Maths content, the execution is mechanical with no novel insight required, making it slightly easier than average overall. |
| Spec | 4.05c Partial fractions: extended to quadratic denominators4.06b Method of differences: telescoping series |
2. (a) Express $\frac { 2 } { ( 2 r + 1 ) ( 2 r + 3 ) }$ in partial fractions.\\
(b) Hence prove that $\sum _ { r = 1 } ^ { n } \frac { 2 } { ( 2 r + 1 ) ( 2 r + 3 ) } = \frac { 2 n } { 3 ( 2 n + 3 ) }$.\\
\hfill \mbox{\textit{Edexcel FP2 Q2 [5]}}