OCR MEI FP1 2006 June — Question 6 7 marks

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2006
SessionJune
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicProof by induction
TypeProve summation with exponentials
DifficultyStandard +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.
Spec4.01a 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]

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]}}