| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2020 |
| Session | May |
| Marks | 7 |
| Topic | Proof by induction |
| Type | Prove polynomial divisibility property |
| Difficulty | Standard +0.3 This is a straightforward proof by induction requiring standard steps: verify base case n=1, assume true for n=k, prove for n=k+1 by expanding f(k+1)-f(k) and showing it's divisible by 6. The algebra is routine and the divisibility argument is mechanical, making this slightly easier than average but still requiring proper inductive structure. |
| Spec | 4.01a Mathematical induction: construct proofs |
7.
Prove by induction that $\mathrm { f } ( n ) = n ^ { 3 } + 3 n ^ { 2 } + 8 n$ is divisible by 6 for all integers $n \geq 1$\\
\hfill \mbox{\textit{SPS SPS FM 2020 Q7 [7]}}