| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2020 |
| Session | June |
| Marks | 6 |
| Topic | Proof by induction |
| Type | Prove summation formula |
| Difficulty | Standard +0.3 This is a straightforward proof by induction with a summation formula. The base case is trivial, and the inductive step requires standard algebraic manipulation to show the formula holds for n+1. The factorization is relatively clean and the question follows a standard template with no novel insights required, making it slightly easier than average. |
| Spec | 4.01a Mathematical induction: construct proofs |
10.
Prove by induction that for $n \in \mathbb { Z } ^ { + }$
$$2 \times 4 + 4 \times 5 + 6 \times 6 + \ldots + 2 n ( n + 3 ) = \frac { 2 } { 3 } n ( n + 1 ) ( n + 5 )$$
\hfill \mbox{\textit{SPS SPS FM 2020 Q10 [6]}}