| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2007 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof by induction |
| Type | Prove summation with exponentials |
| Difficulty | Moderate -0.3 This is a standard proof by induction of a geometric series sum, which is a routine FP1 exercise. While induction proofs require careful structure and algebraic manipulation, this particular result involves straightforward algebra with powers of 3 and no conceptual surprises, making it slightly easier than an average A-level question overall. |
| Spec | 4.01a Mathematical induction: construct proofs |
Prove by induction that $\sum_{r=1}^{n} 3^{r-1} = \frac{3^n - 1}{2}$. [6]
\hfill \mbox{\textit{OCR MEI FP1 2007 Q7 [6]}}