| Exam Board | SPS |
|---|---|
| Module | SPS ASFM Mechanics (SPS ASFM Mechanics) |
| Year | 2021 |
| Session | May |
| Marks | 6 |
| Topic | Proof by induction |
| Type | Prove divisibility |
| Difficulty | Moderate -0.3 This is a straightforward proof by induction with a standard divisibility statement. The base case is trivial (n=1 gives 2+3=5), and the inductive step requires only routine algebraic manipulation to factor out 5 from f(k+1). While it requires proper proof technique, it's a textbook-style induction problem with no conceptual surprises, making it slightly easier than average. |
| Spec | 4.01a Mathematical induction: construct proofs |
Prove by induction that, for $n \in \mathbb{Z}^+$,
$$f(n) = 2^{2n-1} + 3^{2n-1} \text{ is divisible by 5}.$$
[6]
\hfill \mbox{\textit{SPS SPS ASFM Mechanics 2021 Q2 [6]}}