| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2006 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof by induction |
| Type | Prove summation with exponentials |
| Difficulty | Standard +0.3 This is a straightforward proof by induction with a simple geometric series. The formula is given, requiring only verification of base case and inductive step with routine algebraic manipulation. While it's Further Maths content, this is a standard textbook induction problem with no conceptual challenges, making it slightly easier than average overall. |
| Spec | 4.01a Mathematical induction: construct proofs |
Prove by induction that $3 + 6 + 12 + \ldots + 3 \times 2^{n-1} = 3(2^n - 1)$ for all positive integers $n$. [7]
\hfill \mbox{\textit{OCR MEI FP1 2006 Q6 [7]}}