| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2023 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Proof by induction |
| Type | Prove summation with logarithms |
| Difficulty | Challenging +1.2 This is a Further Maths proof by induction involving logarithms and factorials. While the algebraic manipulation requires careful handling of log laws and factorial expressions, the inductive structure is standard. The key insight—recognizing that the product of odd numbers relates to factorials—is moderately challenging but within reach for Further Maths students who have practiced similar problems. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules4.01a Mathematical induction: construct proofs |
\begin{enumerate}
\item Prove by induction that for all positive integers $n$
\end{enumerate}
$$\sum _ { r = 1 } ^ { n } \log ( 2 r - 1 ) = \log \left( \frac { ( 2 n ) ! } { 2 ^ { n } n ! } \right)$$
\hfill \mbox{\textit{Edexcel F1 2023 Q9 [6]}}