| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2017 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Proof by induction |
| Type | Prove summation with fractions |
| Difficulty | Standard +0.8 This is a Further Maths proof by induction with partial fractions. While the inductive framework is standard, students must decompose the fraction 2/[r(r+1)(r+2)] into partial fractions, handle telescoping sums correctly, and perform algebraic manipulation in the inductive step. The three-factor denominator and the specific form of the result make this more demanding than typical single-level A-level induction proofs, but it remains a recognizable F1 exercise type. |
| Spec | 4.01a Mathematical induction: construct proofs |
3. Prove by induction that for $n \in \mathbb { Z } ^ { + }$
$$\sum _ { r = 1 } ^ { n } \frac { 2 } { r ( r + 1 ) ( r + 2 ) } = \frac { 1 } { 2 } - \frac { 1 } { ( n + 1 ) ( n + 2 ) }$$
\hfill \mbox{\textit{Edexcel F1 2017 Q3 [5]}}