Higher November 2017 Paper 1 Q17
17 \(n\) is an integer.
Prove algebraically that the sum of \(\dfrac{1}{2}n(n + 1)\) and \(\dfrac{1}{2}(n + 1)(n + 2)\) is always a square number. (2)
| Answer | Mark | Notes |
|---|---|---|
| Completes proof | M1 | Expands both expressions eg \(\dfrac{1}{2}(n^2 + n + n^2 + n + 2n + 2)\) or \(n^2 + n\) and \(n^2 + n + 2n + 2\) or factorises \(\dfrac{1}{2}(n+1)(n+n+2)\) |
| C1 | Completes proof with explanation and reference to \((n+1)^2\) |