| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Proof by induction |
| Type | Prove summation with exponentials |
| Difficulty | Standard +0.3 This is a standard proof by induction for a summation formula. While it's Further Maths content, the structure is routine: verify base case, assume for n=k, prove for n=k+1 using algebraic manipulation. The algebra requires careful handling of powers of 2 but follows a predictable pattern. Slightly easier than average due to its formulaic nature, though the FP1 context means students should be comfortable with induction mechanics. |
| Spec | 1.04g Sigma notation: for sums of series4.01a Mathematical induction: construct proofs |
Prove by induction that, for $n \in \mathbb{Z}^+$, $\sum_{r=1}^{n} r 2^r = 2\{1 + (n - 1)2^n\}$.
[5]
\hfill \mbox{\textit{Edexcel FP1 Q32 [5]}}