Moderate -0.5 This is a straightforward application of standard summation formulae requiring expansion to quadratic and linear terms, then direct substitution of known results. While it's Further Maths content, it's a routine first question requiring only algebraic manipulation and formula recall with no problem-solving insight needed.
Expand and attempt to use standard series, at least one used correctly
Any two terms correct, may be unsimplified
A1
Any two terms correct
All terms correct
A1
All terms correct
\(\frac{1}{2}n(2n+3)(n-1)\) or \(n(n+\frac{3}{2})(n-1)\)
DM1
Attempt to find 3 factors
Obtain correct answer
A1
Obtain correct answer
[5]
## Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{1}{2}n(n+1)(2n+1) - n(n+1) - n$ | M1* | Expand and attempt to use standard series, at least one used correctly |
| Any two terms correct, may be unsimplified | A1 | Any two terms correct |
| All terms correct | A1 | All terms correct |
| $\frac{1}{2}n(2n+3)(n-1)$ or $n(n+\frac{3}{2})(n-1)$ | DM1 | Attempt to find 3 factors |
| Obtain correct answer | A1 | Obtain correct answer |
| **[5]** | | |
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